This article reports on the development and tests of the adaptive semi-implicit scheme (ASIS) solver for the simulation of atmospheric chemistry. To solve the ordinary differential equation systems associated with the time evolution of the species concentrations, ASIS adopts a one-step linearized implicit scheme with specific treatments of the Jacobian of the chemical fluxes. It conserves mass and has a time-stepping module to control the accuracy of the numerical solution. In idealized box-model simulations, ASIS gives results similar to the higher-order implicit schemes derived from the Rosenbrock's and Gear's methods and requires less computation and run time at the moderate precision required for atmospheric applications. When implemented in the MOCAGE chemical transport model and the Laboratoire de Météorologie Dynamique Mars general circulation model, the ASIS solver performs well and reveals weaknesses and limitations of the original semi-implicit solvers used by these two models. ASIS can be easily adapted to various chemical schemes and further developments are foreseen to increase its computational efficiency, and to include the computation of the concentrations of the species in aqueous-phase in addition to gas-phase chemistry.

In chemical transport models (CTMs) or general circulation models (GCMs), the description of atmospheric chemistry has rapidly increased in complexity. Early model developments were devoted to the study of the stratospheric and upper tropospheric compositions focusing on the gas-phase reactions that control the ozone distribution. Emphasis has since been put on tropospheric chemistry due to its oxidant properties and its possible impact on climate via the lifetime of several greenhouse gases and the distribution of secondary-formed aerosols.

Large-scale models now include chemical schemes that deal with about a hundred species and with several hundred reactions in gas phase and in heterogeneous phases (solid and liquid). Most of those species undergo transport processes, like advection, diffusion, and convection. As a result the models include the solution of complex coupled systems which cannot be handled in a single operator. In practice the various processes are decomposed in a series of operators that are solved numerically in sequence. For example, the time evolution of the species are first calculated taking into account advection, then diffusion, convection, and so on. Among these processes the evolution of the species due to chemical transformations is a key component of the models.

The models have to solve coupled ordinary differential equation (ODE) systems
that describe the adopted chemical mechanism. These ODE systems are of the
non-linear form:

Adequate algorithms must then be used to deal with the stiffness of the ODE systems and to achieve good accuracy. Existing algorithms vary in formulation and complexity. They can be classified as explicit or implicit schemes (see, e.g., Sandu et al., 1997a), and use single or multistep or multistage methods (Sandu et al., 1997b). Multistage implicit algorithms based on Gear (Hindmarsh, 1980) and Rosenbrock (Hairer and Wanner, 1991) formulations are the most accurate but require a significant amount of computation, which limits their use in comprehensive atmospheric chemistry models. To reduce the computational cost the solver described in the present article is based on a one-step implicit algorithm. Its characteristics are detailed in the next sections along with comparisons with other implicit schemes.

For atmospheric applications some numerical properties of those algorithms
should be particularly sought for the following:

The integration of Eq. (1) cannot be done using a simple one-step explicit
scheme with the left-hand-side terms evaluated at time

One possibility to increase the time step is to treat part of the right-hand
side of Eq. (1) implicitly, for instance keeping the evaluations of

One way to alleviate this problem is to discretize Eq. (2) fully implicitly
in time using the simple Euler-backward (EB) method:

The implicit methods described above to solve the ODE chemical system are all
one time step: only concentrations at time

Mass-conserving, multistep or multistage, and high-order accurate implicit methods exist to solve the ODE stiff system. Among the methods based on BDF, Gear's predictor–corrector method has been adapted to atmospheric chemical systems, for example, the SMVGEAR code (Jacobson and Turco, 1994) implemented in the GEOSCHEM CTM (Bey et al., 2001). More recently, the Rosenbrock's method (Rosenbrock, 1963) is becoming widely used in atmospheric chemistry modeling (Sandu et al., 1997b) despite the fact that its computational cost is still rather high compared to approaches based on low-order BDF methods. The implementation in chemical models of Rosenbrock's and other high-order methods has been eased by the development of the Kinetic PreProcessor (KPP) by Sandu and Sander (2006), which allows the choice of an integration method and generates the adequate codes accordingly.

When the chemical scheme involves more than 100 species and over 200 reactions, the implicit multistage methods are still
computationally expensive, especially if they are to be used within global
3-D models with horizontal resolutions on the order of

The approach adopted for ASIS is to restrict the algorithm to a single
implicit step combined with a specific evaluation of the Jacobian matrix of
the chemical fluxes,

The first term of the right-hand side corresponds to the chemical productions
or destructions due to first-order reaction rates with constants

The time discretization of Eq. (4) is then performed with a semi-implicit
scheme for the first term adapted to each reaction and time step and an implicit
discretization for the second one, and the external tendencies are assumed to
be constant over the time step

Equation (5) can be recast with terms containing species concentrations at
time

Compared to other one-step semi-implicit schemes like SIS (i.e., Ramarosson
et al., 1994), one specificity of our scheme lies in the evaluation of

Furthermore, the use of Eq. (9) to calculate

The oscillations from odd to even time steps that can appear in the numerical
solution of Eq. (6) when the semi-implicit scheme is centered and symmetrical
(i.e., Suhre and Rosset, 1994), as would be if the fixed value

Since the largest terms contributing to the evolution of the shortest-lived species are treated implicitly, the system increases in stability. Larger time steps can be used and positive values for the concentrations are more easily preserved.

All the species are treated in the same manner without any a priori considerations on lifetimes or abundances.
For instance in the case of the Earth composition, O

Our baseline option is to use the direct solver DGESV of the Lapack library that solves system (6) by lower–upper (LU) decomposition. Therefore no extra specific routine associated with the chemical mechanism is needed and the optimization on the computer used is left to the implementation of the Lapack library. As reported below, this option works well and gives accurate results even for comprehensive mechanisms involving hundreds of species or more.

To reduce the computational cost, other options for the solution of the linear system have been investigated. Two iterative solvers have been tested. The first one is an implementation of the Gauss–Seidel algorithm. This algorithm has been used with success to solve stiff systems from chemical kinetics (Verwer, 1994; Menut et al., 2013). For the cases studied in the following sections, the Gauss–Seidel algorithm was found to be efficient with a good rate of convergence in most cases. Although in specific situations where the system is largely driven out of equilibrium, for instance during day–night transitions and for large surface emissions, the number of iterations could increase by 1 order of magnitude to obtain the required accuracy.

A second iterative algorithm has been implemented, the generalized minimal
residual method (GMRES). The method approximates the solution by a vector in
a Krylov subspace with minimal residual norm. The Arnoldi iteration algorithm
is used to find this vector. The GMRES method was developed by Saad and
Schultz (1986) and further described by Saad (2003). In order to accelerate
the convergence, preconditioning techniques are used. An efficient technique
was obtained by introducing the matrix

Since the time discretization adopted to solve system (7) is first-order
accurate, the choice of the time step

Therefore a variable stepsize strategy has to be implemented with the time
interval

The choice of

For the first iteration species, concentrations at two consecutive times and
a first-guess time step are needed. To avoid storing concentrations at
consecutive times we assume that at the beginning of the iterative process
the system is in a steady state,

To validate and evaluate the performances of ASIS and the associated
numerical codes, several case studies have been used. All the cases reported
in this section are based on the RACMOBUS chemical scheme used within the
MOCAGE CTM. RACMOBUS is a combination of the REPROBUS scheme adapted to the
stratosphere and the free troposphere (Lefèvre et al., 1994) and the RACM
scheme (Stockwell et al., 1997) that treats the urban polluted earth
atmosphere with the addition of volatile organic compounds (VOCs) and their
degradation products. Table 1 lists the chemical species taken into account;
the overall scheme includes about 120 species linked by 200 gas-phase
reactions and photodissociations. The photodissociation rates are calculated
every 15 min using the tropospheric ultraviolet and visible (TUV) radiation
model version 5.2 (Madronich and Flocke, 1998) for conditions corresponding
to the equinox at

Two test cases are used to evaluate the accuracy and performance of the ASIS
scheme. The first one is based on the FLUX test case described by Crassier et
al. (2000). It corresponds to a ground-level situation in a polluted urban
area. The list of species and fluxes emitted at the surface is given in
Table 2. The emissions are injected in a boundary layer with a 2000 m
constant thickness weighted by an emission factor of 0.6. This leads to a
constant tendency

The second case, STRATO, is representative of situations encountered in the middle stratosphere. The initial concentrations for this case are given in Table 3. The atmospheric temperature is 215 K and the pressure is 50 hPa. For both cases the integration starts at midnight and stops 24 h after, and the photodissociation rates are updated every 15 min.

List of species used for the box-model simulations. The upper part of the table lists the species active in the free troposphere and the stratosphere. The lower part lists additional VOC species or generic species involved in the RACM mechanism (Stockwell et al., 1997).

VOC emissions in the FLUX test case.

Initial conditions for the FLUX and STRATO test cases.

To assess the performances of ASIS, two reference simulations have been
obtained for the FLUX case using Rosenbrock's and Gear's BDF solvers
(referred to hereafter as R1 and G1). Those solvers use the “ode23s”
and “ode15s” codes, respectively, from the Matlab ODE suite (Shampine and Reichelt, 1997;
Ashino et al., 2000). For the Rosenbrock's scheme a three-stage algorithm is used
and the simulations are third-order accurate. For the Gear's scheme the third-order accurate option was also chosen. In the most accurate simulations, R1
and G1 (see Table 4), the relative tolerance RTOL is set to 0.001 and the
absolute tolerance ATOL equals

The same FLUX case is integrated using the ASIS solver. In a first simulation noted A1, ASIS uses a RTOL value of 0.001 and a minimum time step of 1 s. For the solution of the linear system associated with ASIS, the DGESV code of the Lapack library is used. To compare with the Rosenbrock's solver a second simulation A2 has been obtained with the same settings as A1 but with a higher relative tolerance value of 0.01, and a third one A3 with a tolerance value of 0.025. For all experiments the FLUX case is integrated over 24 h. The settings used in the overall simulations are given in Table 4.

Figures 1 and 2 show the evolution of some key species for each experiment and the relative differences from the R1 experiment. Those results are representative of all of the species. As expected, the R1, G1, and A1 simulations give very close results. R1 and G1 show relative differences below 0.1 %, consistent with the value chosen for RTOL. A1 results are comparable with differences in the 0.1–0.2 % range, except at the beginning of the simulation when the chemical state is out of equilibrium and during day–night transitions. In those situations the differences between A1 and R1 or G1 can reach 0.5 %. As expected from the choice of a higher value for RTOL, the A2 experiment shows less accuracy but is still in the range of 0.5 % compared to the other experiments. The A3 experiment has differences below 2 % with the other experiments. For most of the atmospheric simulations an accuracy below 1 % is sufficient for the longest-lived species, and even larger values are acceptable for short-lived species if they are transient, given the uncertainties in the representation of the other processes and the inaccuracies introduced by their solution by a series of successive operators.

List of the different settings used by the 0-D model for the FLUX
test case. The mean time step is denoted by

The efficiency of ASIS can be first evaluated by comparison of the mean time steps (Table 4). For simulations R1 and G1 the mean time steps are between 25 and 40 s. Since ASIS uses a first-order scheme to maintain good accuracy, the mean time step is lowered, in the 5 s range for the A1 experiment. However, ASIS is a one-stage scheme (only one linear system is solved by time step) compared to R1 and G1 that need three or more stages. The amount of computation is therefore comparable. When the relative tolerance is increased, the mean time step of ASIS increases. For the A2 experiment it is 25 s, identical to R1, and up to 49 s for A3. Since for most atmospheric simulations a relative tolerance of 0.01 to 0.025 seems to be sufficient, the ASIS solver gives acceptable solutions with less computation than the higher-order schemes.

The efficiency of ASIS in terms of CPU time has been evaluated within the Matlab environment. Table 4 gives the ratio of CPU time used for each simulation relative to the R1 case. The ode23s code used to run the R cases needs the implementation of two subroutines, one that computes the species tendencies and one that gives the Jacobian of the system. If the latter is not provided, the ode23s code computes an approximation of the Jacobian by differentiation and the CPU cost increases by a factor of 2 to 10. As can be seen from Table 4, the CPU cost of ASIS is comparable to or lower than the ode23s cost for relative tolerance values larger than 0.01.

An important point to mention is that within the Matlab environment the CPU
cost does not come from the linear algebra parts of the algorithms but from
the evaluation of tendencies and Jacobian matrices. Therefore it is very
dependent upon the chemical system and the details of the programming of the
associated subroutines. The situation is quite different within the Fortran
environment. With the Fortran version of ASIS the CPU cost for the
calculation of the approximated Jacobian (the matrix

FLUX case. Time evolution of selected species (

FLUX case. Same as Fig. 1 for

For the A experiments, ASIS uses the DGESV code for the solution of the linear
systems. To save computational time two iterative solvers have been tested,
one using the Gauss–Seidel algorithm, the other the GMRES method. Both
solvers used the same criterion for convergence (tolerance for convergence
set to

The results are practically identical to the solution obtained using the DGESV code; the differences between the solutions are below 0.02 % for all the species concentrations. The simulation with the Gauss–Seidel algorithm shows good efficiency in terms of mean number of iterations, but requires 6 to 10 times more iterations when the system is driven out of equilibrium during day–night transitions. Using GMRES was found to be more stable and efficient, with less than 10 iterations needed to solve the linear systems and half as much computational time (using the Fortran version of the code) compared to the simulation using DGESV.

From the simulations of this FLUX case, which is rather representative of situations encountered in polluted earth boundary layers, it can be concluded that the ASIS solver performs well compared to higher-order schemes when moderate accuracy is required. Apart from tolerance parameters and the choice of a minimum time step, no specific tuning is required. The one-step implicit scheme gains in efficiency when coupled to the GMRES iterative solver used for the solution of the linear systems.

The STRATO case differs from the FLUX case in the dominant chemical
regimes involved. In the FLUX case the VOC decomposition during day and night
dominates the system. With the STRATO case the chemistry is dominated by
NO

For this case, two simulations have been performed. The first one, RS1, uses
the Rosenbrock's algorithm with settings similar to experiment R1. For the
second one, AS2, the ASIS solver is used with settings similar to experiment
A2 and with the iterative linear solver GMRES. The two simulations show
results consistent with the findings for the FLUX case. The mean time steps
are very similar for both experiments,

STRATO case. Number of time steps of the ASIS solver for each interval of 15 min in experiment AS2.

In terms of accuracy, the AS2 experiment gives results that depart less than

Equally, the approximations in the Jacobian are efficient to prevent the development of negative mixing ratios. In the two cases FLUX and STRATO, we did not encounter any significant (larger than ATOL) negative values during the course of the simulation, and all the concentrations remain positive at the end of the 15 min intervals before the photodissociation rates are updated.

In summary, the results of the two test cases confirm the properties targeted in the design of ASIS. At the moderate accuracy required for atmospheric simulations, the ASIS solver compares well with higher-order schemes, and limits the computational cost while assuring mass conservation. The next sections illustrate how it performs in more realistic situations with implementations in state-of-the-art global CTMs for Earth and Mars atmospheres.

STRATO case. Time evolution of selected species (

For this study we have used the global version of the MOCAGE CTM with a horizontal resolution of

The reference simulation (referred to hereafter as MR) uses the original solver for
chemistry, an iterative semi-implicit scheme with assumptions of equilibrium
for short-lived species and species lumping for NO

The simulation with the ASIS solver, MA, uses the same configuration for
MOCAGE as MR except that the original chemical solver is replaced by ASIS
with settings similar to experiment A3: RTOL

The characteristics of the ASIS functioning implemented within MOCAGE can be first examined by the diagnostic of the number of sub-time-steps for chemistry. Figure 5 shows this number for three different levels for a date corresponding to 15 September at midday. In the midstratosphere, at 50 hPa, the number of sub-time-steps varies in accordance with what was found for the STRATO test case. At midday or midnight the chemical system is in quasi-steady-state and this number is small, below 3. Close to the terminators, this number increases up to 40–60, highlighting the change of regime of the chemical system when the photodissociation is activated or deactivated. During these transition phases the stiffness of the system increases and the sub-time-steps decrease to maintain the required accuracy. Also barely noticeable is an increase of the number of sub-time-steps over the Antarctic coast at the edge of the polar vortex. In these regions the heterogeneous reactions acting at the surface of polar clouds are activated, driving the concentrations of the chlorine species out of equilibrium. It leads to a reduction of the sub-time-steps to cope with the rapid variations of the chemical composition of the air masses.

In the middle troposphere the same behavior is encountered near the terminators, with a tendency to maintain reduced sub-time-steps during longer periods after sunrise or before sunset (Fig. 5). An increase of the number of sub-time-steps is also encountered over the African continent at low latitudes. Those regions are prone to convective activity, and injection of species by convection is activated, leaving air masses far from chemical steady state. Since the chemical evolution of the species is calculated after the transport processes, ASIS starts with a situation far from a chemical equilibrium and the number of sub-time-steps increases.

At the surface, Fig. 5 shows the same characteristics as in the midtroposphere with an increase of the number of sub-time-steps at the terminators and over the continents. Over the continents the surface emissions play a larger role than convection in destabilizing the chemical system. Within MOCAGE the emissions are calculated according to inventories and deposited in the boundary layer. This is treated as an isolated process that changes the concentrations. As a result ASIS starts with situations out of chemical equilibrium and adopts small sub-time-steps, about 20 s compared to 60 s over the oceans.

Number of sub-time-steps per time step of 15 min in the MA simulation for the 15 September at midday. Three levels are presented representative of the stratosphere (50 hPa), the midtroposphere (540 hPa), and the surface.

Except for noticeable cases that are discussed hereafter, the species
distributions of the simulation with the ASIS solver (referred to hereafter as MA) are close to those
obtained in MR. As an illustration, Fig. 6 shows the zonally averaged
distributions of

In the lower troposphere, examination of the code of the MR simulation
reveals that approximations and steady-state assumptions are made for the
computation of the nighttime

Zonal mean distributions of

Figure 7 shows, for example, the distributions of

Monthly mean distributions of

Another significant difference between MR and MA is found in the simulation
of the ClO

In the air masses prone to heterogeneous reactions on PSC, the composition
changes rapidly at sunrise and non-linear processes, like the formation of

As a result, the MR simulation produces a much more pronounced ozone
depletion over Antarctica than the MA simulation. MR calculates ozone column
contents as low as 100 Dobson Units (DU), whereas the MA simulation maintains
values in the range of 150 DU. This is well illustrated in Fig. 8, which
shows the evolution of the total ozone columns over two Antarctic stations,
Dumont d'Urville and Dome C. For these two stations the measurements done by
SAOZ instruments (Pommereau and Goutail, 1988) at sunrise and sunset are also
presented (data available at

Starting around Julian day 220, the MR and MA simulations start to diverge. Over Dumont d'Urville, the station that sees first the return of the sunlight, the ozone decrease is about 50 % larger in the MR simulation than for MA. By day 260 the ozone column is just above 150 DU whereas it is in the 200 DU range in the MA simulation. Clearly the MA simulation is in better agreement with the SAOZ measurements.

Evolution of the total ozone column over the Dumont d'Urville and Dome C Antarctic stations. The dots are the observations of the SAOZ instrument, the orange line is the evolution calculated in the reference simulation, MR, and the red line the same output from the simulation MA using the ASIS solver.

The same behavior is seen for the Dôme C station. The ozone depletion starts slightly later, around day 240. In the MR simulation the depletion is very pronounced and the ozone column diminishes rapidly in a few days from 240 to 150 DU, and further decreases at a slower rate to reach a minimum of 100 DU at day 260. The MA simulation shows a more continuous decrease from day 240 to 260, with an ozone column reaching a minimum of 150 DU. The MA simulation is here again in very good agreement with the SAOZ observations.

Implementation of the ASIS solver within MOCAGE has thus revealed two
weaknesses of the original model. One problem is in a limitation on the
validity of assumptions made to compute the night-time distribution of the
NO

Clearly the implementation of ASIS within MOCAGE is very beneficial to the model simulations and increases the confidence on the model results. In addition, further evolution of the model with adoption of different chemical schemes or addition of new reactions is very easy with ASIS.

There is, however, a price to pay in terms of computer time. Overall the MA
simulation takes 4.7 times more computational time than the MR simulation.
This number could certainly be decreased by further tuning of the parameters
of the solver, RTOL, ATOL, and

Our experience with ASIS shows that, since various processes are computed by
a series of operators, the solver starts new time steps with situations often
out of chemical equilibrium and must use small sub-time-steps. To alleviate
this, one possibility is that tendencies from these operators would be
computed and stored rather than used to update the species concentrations.
The tendencies can then be used to solve the system though their introduction
in the term

Another issue lies in the parallelization of the computations. In the reference simulation the computational cost is equal for each grid point at a given level and good parallelization is obtained with an equally spaced latitudinal band decomposition (and use of openMP directives). When ASIS is used the computational cost in each grid point depends on the state of the chemical system. As illustrated in Fig. 5, in the stratosphere and upper troposphere more computer time is needed near the terminators and in case of PSC-induced chemistry. In the lower troposphere more computer time is spent in grid points influenced by surface emissions, and convective and boundary-layer transport processes. A speedup of 15 was, however, obtained for the MA simulation on our cluster computer (using 1 node and 16 cores of our BULL computer) with a decomposition that groups more longitudes in the Southern Hemisphere than in the Northern Hemisphere, near the poles. But further tuning would be required if more nodes are to be used. This tuning could vary with season and additional parallelization could be introduced with domain decomposition on the vertical.

To illustrate the versatility of the ASIS solver, we present results of the
implementation of ASIS in the LMD Mars model with photochemistry (Lefèvre
et al., 2004). This Mars GCM describes the evolution of 19 species (Table 5)
by means of 54 chemical or photolytic reactions. The bulk atmosphere of Mars
is composed of 95 %

List of species used in the Mars model simulations.

In the standard version described in Lefèvre at al. (2004), the LMD GCM
with photochemistry uses the EB method expressed in Eq. (3) to solve its
chemical system. As mentioned earlier, this method is positive, stable, and
can be computationally effective but does not maintain mass conservation.
Iterative evaluations of

Comparison of the Euler-backward (EB) and ASIS solvers applied to
the Mars box-model version. The left column shows the mixing ratios of

Figure 9 compares the results obtained with the EB and ASIS solvers applied
to a box-model version of the LMD Mars model. The atmospheric
pressure (temperature) is 5.4 hPa (212 K) at the surface and 0.2 hPa (140 K) at
30 km. In both cases the integration starts at noon, and stops after one
Martian solar day of 24 h 40 mn. The photodissociation rates are calculated
every 15 min using the TUV radiation model adapted to Mars. The time step of
the EB solver is fixed to

At the surface, Fig. 9 shows that the ASIS solver calculates an

The box-model simulations at 30 km are performed at the hygropause level
where the production rate of HO

Number of sub-time-steps per time interval of 15 min in the LMD Mars
GCM in northern spring (instantaneous result at solar longitude Ls

In its 3-D implementation, ASIS is called by the LMD GCM at
each physical time step

Figure 10 shows the number of sub-time-steps per physical time step of 15 mn
in a GCM simulation of northern spring (Ls

Distribution of

Figure 11 compares at 30 km the results of GCM simulations using either the
EB or the ASIS solver. Both schemes give distributions of

The ASIS solver has been designed to cope with the various situations encountered within the numerical simulation of the atmospheric chemistry. The main properties of the solver are mass conservation, an approximation of the Jacobian matrix of the chemical fluxes that stabilizes the associated system of differential equations, a time-stepping varying module to control accuracy, and a code implementation that allows an easy adaptation to various chemical schemes. In box-model test cases, the numerical solutions obtained with the ASIS solver were found to be in good agreement with those of multistep algorithms like Rosenbrock's and Gear's methods.

The ASIS solver has been implemented in 3-D models of the Earth (MOCAGE) and
Mars (LMD model) planets. The results with MOCAGE using ASIS reveals two
weaknesses of the original semi-implicit solver. One is related to the
calculation of the partitioning of the NO

The model simulations show the benefit of using a chemical solver with good properties such as mass conservation and controlled accuracy. This objective can be achieved using multistep high-order algorithms, but the computational cost of those schemes increases rapidly with the number of species considered. Since ASIS is implicit and one-step, a single linear system has to be solved for each iteration. For this, direct or iterative algorithms can be used. The direct methods based on LU decomposition see their computational cost increasing at least quadratically with the number of species, whereas the cost of iterative solvers increases rather linearly. Within ASIS we found that the GMRES iterative algorithm is stable and efficient, and is competitive in terms of CPU cost compared to the direct DGESV algorithm.

In atmospheric models the computational cost is a key issue, and
parallelization of the computations must be efficient to reduce the elapsed
time spent for the simulations. As pointed out earlier, the amount of
computation spent by ASIS to solve the chemical system can vary significantly
from one grid point to another. This renders the work balancing of tasks more
difficult if a domain decomposition strategy is adopted to implement the
parallelization. As already discussed with the surface emissions, one
possibility to diminish the number of iterations and the heterogeneity in the
CPU used at each grid point is to account for nonchemical tendencies in the
species continuity equations (term

The present version of the ASIS solver addresses the evolution of the concentrations in gas phase only. For some applications the aqueous phase associated with the presence of clouds must be also considered (e.g., Leriche et al., 2013). The chemistry module has to solve both gaseous- and aqueous-phase chemistry as well as mass transfer reactions between gas and liquid phases. There is a priori no difficulty in adding the prognostic concentrations in the water phase to the system of equations and making a linearization similar to what is done in Eq. (6). However, the addition of aqueous reactions tends to increase the stiffness of the numerical ODE (Audiffren et al., 1998), so the performances of ASIS could diminish and may result in reduced time steps and increased computer time.

In conclusion, the ASIS solver can deal with many situations encountered in modeling atmospheric chemistry for a computational cost affordable by CTMs and GCMs that include comprehensive chemical schemes. Evolution of the ASIS solver to treat aqueous-phase chemistry is planned in the near future.

The Fortran code to run the ASIS solver on the FLUX case
described is Sect. 3 is available as a Supplement to the present article and
can be downloaded from the CERFACS server (

The code associated with the chemistry model includes subroutines that define the mechanism and those more specific to the ASIS solver. At this stage we have not developed an external driver or a pre-processor that would generate specific codes based on the adopted mechanism. This choice was done because our experience is that the maintenance of the driver outputs can be somewhat cumbersome when many developers work in parallel on a CTM. In addition, the code generated by the driver must be optimized often for the computer used and adapted to the CTM. It is therefore not used directly, which introduces further constraints on the maintenance of the overall code.

Our approach is rather to define the mechanism by a limited number of fortran
subroutines that are simply added to the other routines of the code. The

1/ A

2/ A + A

3/ a A + b B

The first group includes photodissociations and thermal decomposition of the
species. This classification is done in order to optimize the calculation of
the terms of the matrix

Once the definition of species and reactions is completed, the calculation of
the matrices (Eq. 7) is done by the

The authors declare that they have no conflict of interest.

This work was supported by the Monitoring Atmospheric Composition and Climate
(