The convective transport module, CVTRANS, of the ECHAM/MESSy Atmospheric Chemistry (EMAC) model has been revised to better represent the physical flows and incorporate recent findings on the properties of the convective plumes. The modifications involve (i) applying intermediate time stepping based on a settable criterion, (ii) using an analytic expression to account for the intra-time-step mixing ratio evolution below cloud base, and (iii) implementing a novel expression for the mixing ratios of atmospheric compounds at the base of an updraft. Even when averaged over a year, the predicted mixing ratios of atmospheric compounds are affected considerably by the intermediate time stepping. For example, for an exponentially decaying atmospheric tracer with a lifetime of 1 day, the zonal averages can locally differ by more than a factor of 6 and the induced root mean square deviation from the original code is, weighted by the air mass, higher than 40 % of the average mixing ratio. The other modifications result in smaller differences. However, since they do not require additional computational time, their application is also recommended.

A key process in global modeling of atmospheric chemistry and climate is the
vertical exchange of air

Here, we revise the parameterization in the convective transport module

In Sect.

In this study we apply and improve version 2.50 of the MESSy (Modular Earth Submodel System) framework

The moist convective transport for tracers other than water is calculated by
the CVTRANS submodel

In the algorithm, the properties of the air that detrains from the plumes are
determined according to

Note that (only) the mass fluxes and mixing ratios in the up- and downdraft plumes are specified at the top interface of the indexed grid cell.

The mixing ratios in the plumes, which are also needed for
Eqs. (

If the vertical mass fluxes are very strong,

Near the convective cloud base, we can account for recirculation effects
within a single time step in a computationally less inexpensive manner by
applying an analytic solution for the sub-cloud mixing ratio evolution. At
cloud base level

As a third modification, we include a recently published parameterization for
the vertical transport of chemical reactants at the convective cloud base

Optional MESSy submodels that are enabled for the numerical experiments.

We performed numerical simulations with EMAC to quantify the impact of
the various code modifications. In these simulations, the MESSy
submodels that are listed in Table

Convective transport is evaluated using passive tracers with exponential
decay and a constant spatially uniform emission pattern. The lifetimes of
these tracers,

Description of the different numerical experiments. Listed are the
differences in settings between the simulations and required computational
time (in CPU hours). If

Multiple numerical experiments have been performed. Experiments whose name
start with “ORG” do not use the intermediate time stepping, but if an
experiment name starts with an “I”, it does employ the intermediate time
stepping and it is followed by a three-digit number that is equal to

Weighted root mean square deviations between two numerical experiments. Results, expressed as percentages of the respective air-mass-weighted mixing ratios, are listed for the seven tracers.

While evaluating induced differences, only data averaged over 2001 is
considered. Hence, we do not consider short-term fluctuations but
rather focus on long-term shifts related to the different convective
transport representations. For quantification, the root mean square
deviation (RMSD) over the numerical grid is used, weighted by the air
mass,

In Sect.

The weighted root mean square deviations between different numerical
experiments are listed in Table

As can be seen from Table

Horizontal distribution of the decaying scalar with
a lifetime of 1 day, averaged over 2001 at 700

In Fig.

In the ORG numerical experiment, convective transport is capped when the
upward mass flux transports more air in one time step than is present in
the underlying grid cell. This nonphysical capping of the flow can be removed
when intermediate time steps are enabled. As shown in
Fig.

Decaying scalar with a lifetime of 1 day, averaged zonally
and over 2001. Shown are

The substantial change in the representation of convective transport
with intermediate time steps is also clear from
Fig.

Note from Table

By applying the analytic expression for the (sub-)time step average mixing
ratio below the cloud base of Eq. (

Since part of the air at the updraft plume base now originates from the
environment above cloud base, the effect of vertical mixing by convective
transport is reduced. This results in stronger vertical gradients with higher
mixing ratios near the surface and higher mixing ratios in the upper
troposphere, as confirmed in Fig.

As most clearly illustrated by the RMSD between ORG and ORGA in
Table

Relative difference in zonally and 2001 averaged mixing ratios for ORGA compared to ORG. Results are shown for the tracer with a lifetime of 1 day.

Root mean square deviations of the 2001 averaged mixing
ratios compared to reference case I001 for decaying scalars with
a lifetime of

While the dynamics are best represented by using intermediate time stepping
with a low

The RMSD is roughly proportional to the value of

Applying the analytic expression does not change the computational time
substantially but always improves the results when intermediate time
stepping is applied. This improvement reduces the RMSD only by a small amount
(

As we find that setting

Here we apply the improved representation for mixing ratios in the base of
the updraft plume that was presented by

Relative difference in zonally and 2001 averaged mixing ratios
for UPDP compared to I050A. Results are shown for the tracers with
lifetimes of

Relative difference in the 2001 averaged mixing ratio of the
atmospheric tracer with a lifetime of 1 day for CC compared to
I050A. Results are shown for

The low deviations are most likely related to the limited vertical mixing
ratio gradients around the cloud base. Except for a

As indicated in Sect.

Due to the larger area, the plumes transport a smaller fraction of the
affected air mass and there are less recirculation effects. Therefore, the
vertical transport from the lower cloud layers to the upper cloud layers
becomes more effective and especially higher mixing ratios are found in the
upper troposphere, as shown in Fig.

In total, the effect of using a different convective cloud cover definition
is substantial, with RMSD values ranging from 4 (for

We presented various modifications to the CVTRANS module in the EMAC model to update and revise the representation of convective transport of atmospheric compounds. The new, optional functionality consists of (i) intermediate time stepping when updraft mass fluxes are too strong compared to the air mass in individual grid cells, (ii) an analytic expression that accounts for the intra-(sub-)time-step evolution of air properties below the base of the convective plume, and (iii) a recently published parameterization for the mixing ratios of atmospheric compounds at the updraft base.

It was demonstrated that applying the intermediate time stepping results in
a substantial difference in atmospheric mixing ratios, even when averaged
over 2001. The most important effect turned out to be that physical flows no
longer need to be capped due to numerical limits. For high values of

Even though the analytic expression and updated plume base mixing ratios are
not as important as intermediate time stepping and only result in root mean
square deviations in the temporally averaged mixing ratios of less than
1 % of the air-mass-weighted mixing ratios, these improvements come
without extra computational cost. Furthermore, these metrics were determined
for averaged mixing ratios over 2001, while local, instantaneous mixing
ratios will likely differ more strongly. This will be of importance when
comparing model data directly with time-dependent observations. For future
numerical experiments we therefore recommend to enable all three
modifications. Only when intermediate time stepping is disabled should the analytic
expression not be applied to prevent a further underestimation of the
convective transport. The optimal setting of

As a future development of the convective transport, the current
“leaky pipe” representation could be further investigated. In the
current implementation, at every individual time step an independent
realization of the convective updrafts and downdrafts is calculated. This
could be updated to a plume that evolves in time, similar to the
environmental air. Furthermore, it would be worthwhile to further
quantify, and subsequently apply, the correct value for

The Modular Earth Submodel System (MESSy) is being continuously further
developed and applied by a consortium of institutions. The usage of
MESSy and access to the source code is licensed to all affiliates of
institutions that are members of the MESSy Consortium. Institutions
can be a member of the MESSy Consortium by signing the Memorandum of
Understanding. More information can be found on the MESSy Consortium
website (

The authors thank Jordi Vilà-Guerau de Arellano and Martin Sikma
for their feedback during this project. We further wish to
acknowledge the use of the Ferret program
(