Inaccurate representation of mixing in chemistry transport models, mainly suffering from an excessive numerical diffusion, strongly influences the quantitative estimates of the stratosphere–troposphere exchange (STE). The Lagrangian view of transport offers an alternative to exploit the numerical diffusion for parametrization of the physical mixing. Here, we follow this concept and discuss how to extend the representation of tropospheric transport in the Chemical Lagrangian Model of the Stratosphere (CLaMS).

Although the current transport scheme in CLaMS (v1.0) shows a good ability to represent transport of tracers in the stably stratified stratosphere (Pommrich et al., 2014, and the references therein), there are deficiencies in the representation of the effects of convective uplift and mixing due to weak vertical stability in the troposphere. We show how the CLaMS transport scheme was modified by including additional tropospheric mixing and vertical transport due to unresolved convective updrafts by parametrizing these processes in terms of the dry and moist Brunt–Väisälä frequencies. The regions with enhanced convective updrafts in the novel CLaMS simulation covering the 2005–2008 period coincide with regions of enhanced convection as diagnosed from the satellite observations of the outgoing longwave radiation (OLR).

We analyze how well this approach improves the CLaMS representation of

Modeling of transport from a Lagrangian perspective
has gained increasing popularity in the last few
decades, and not only within the atmospheric community. The chance to avoid,
or at least to minimize, the numerical diffusion ever present in
Eulerian numerical schemes is the strongest motivation
for the Lagrangian formulation of transport.
Despite the obvious advantage of the Lagrangian view separating
mixing from the advective part of transport, only very few Lagrangian
chemical transport models (CTMs) with explicit mixing exist so far

In this paper, the 3-D version of the Chemical Lagrangian Model of the Stratosphere (CLaMS)
will be used

However, in the current version of CLaMS v1.0

One of the widely used parameters quantifying instabilities
is the gradient Richardson number,

In the stratosphere, where the flow is characterized by
high static stability, only almost-isentropic deformations driven by the horizontal
strain and vertical shear are considered in the current version of CLaMS v1.0
(

Generally, CLaMS tropospheric tracers like CO or

Figure

The different shades of blue quantify the
annual mean of the e90 tracer mixing ratios (calculated for 2007) as a function
of latitude and log-pressure altitude and are derived from the current version
of CLaMS v1.0 described in

Similar to WACCM, the artificial e90 tracer, with a constant

In this paper, we aim to parametrize the unresolved
processes like convective updrafts and tropospheric mixing whose representations in global reanalysis data are uncertain

In the next section, we describe the properties and mean distributions of
the dry or moist Brunt–Väisälä frequency,

Static stability can be quantified in terms of the (dry) Brunt–Väisälä
frequency (BVF) via

The zonal mean distribution of dry,

To take into account the contribution of latent heat release to the vertical instabilities,

Thus, lowest values of the dry BVF are distinctive for the middle troposphere especially in the
tropics. The minimum in lapse rate,

On the other hand, low values of the moist BVF (i.e., bluish regions with

To extend the CLaMS mixing scheme, we follow two heuristic ideas. First, due to a much lower vertical stability in the troposphere than in the stratosphere, we enhance tropospheric mixing in the model everywhere (dry) vertical stability is sufficiently small. Second, we take into account additional transport driven by convection, especially by deep convection which is not sufficiently resolved in the reanalysis data.

Thus, whereas the first approach is related to changes in the mixing part of CLaMS and affects the nearest neighbors of each Lagrangian air parcel, the second goal is related to changes in the advection part of CLaMS, i.e., modification of the trajectory calculation. Both extensions should be driven by instabilities quantified in terms of the dry and moist BVFs, respectively, which were introduced in the previous section. By including such a revised transport scheme, we seek a better representation of transport in the free troposphere, which also likely improves the performance of the model within the UTLS region. Because all our changes are confined to the troposphere, we expect a weak influence on stratospheric transport in CLaMS which has been successfully validated in many previous studies. Furthermore, the scheme should not give a heavy burden on the computation time compared to the current version of CLaMS. Before going into the details, we shortly describe the standard version of CLaMS (in the following denoted as the reference setup).

As the reference, we use the 2005–2008 time slice of the 40-year CLaMS transient simulation
starting on 1 January 1979 and driven by the horizontal winds and diabatic heating rates (vertical velocities)
derived from the ERA-Interim reanalysis

The vertical coordinate

For

Thus, because

In the default mixing scheme, CLaMS uses the integral deformations

In the following, we assume that the additional tropospheric mixing should be triggered whenever
the corresponding value of

Mixing driven by vertical instability and strong wind shear.
The profile on the left side is an idealized

Figure

Commonly, convection is understood as a vigorous vertical updraft
resulting from instabilities in the vertical temperature and water distribution profiles,
preferably connecting the PBL with the free troposphere and is schematically shown in Fig.

Convection starts on relatively small horizontal scales on the order of
a few kilometers and is mainly driven by the latent heat release of
the gaseous and liquid water content. Such diabatic processes may lift a large amount of air.
The respective upward mass flux is traditionally denoted as an updraft (thick upward red arrow
in Fig.

The reverse diabatic mass transport, the so-called downdraft, is related to the evaporation of water or melting of ice and is in general much smaller than the original convective updraft (thin blue arrows). A much larger part of the downward mass flux, the so-called subsidence, occurs on much larger horizontal scales of the order of 10–100 km, or even larger if Rossby waves or gravity waves are induced by convection (thick downward red arrows). A significant part of subsidence results mainly from longwave cooling of radiatively active water vapor which is vertically transported and freeze-dried within the convective tower and subsequently spread horizontally at the level of the main convective outflow. Note that the horizontal scale of this outflow region is at least 1 order of magnitude larger than the horizontal extension of the convective tower at the ground.

It is generally believed that the exchange of mass driven by deep convection can efficiently inject the air masses from
the PBL into the upper troposphere or even, although very rarely, into the lower stratosphere

We now present an alternative method to enhance upward transport for conditionally unstable
air parcels with

Following

Color coded is the fraction of ERA-Interim time steps (6 h frequency) within a season when the criterion triggering
the deep convection scheme is fulfilled at CLaMS air parcels within the lowest layer of the model

To illustrate how such a parametrization works, the zonally resolved fraction of events with

Our second condition is related to the question of whether every conditionally unstable air
parcel is a source of convection which should be taken into account. This question
is also related to the fact that the number of air parcels in CLaMS is not strictly
conserved but kept roughly constant within about

The probability distribution function (PDF, in units of % K

To estimate the influence of our convection parametrization on the mass budget, we
calculate the annually and globally averaged mass fluxes due to parametrized convective updrafts (for details
see Appendix

A possible explanation for this deficit can be related to the fact that the horizontal resolution of
the ERA-Interim reanalysis (roughly 80 km) does not sufficiently resolve the convective towers (which are of the order of 1 km)
but does better resolve the large-scale subsidence which may be better reproduced in the ERA-Interim diabatic
vertical velocities. Thus, our parametrization aims to close this imbalance
by including some additional convective updrafts. The results show that qualitatively our
simple approach roughly balances such a deficit and there is still some potential to enhance the strength
of parametrized convection. At least the influence of our parametrization on the mass budged is comparable
with “intrinsic uncertainties” in the mass budget of the reanalysis itself. Following the procedure
described in

Finally, it should be mentioned that our Lagrangian parcels are still too large
(around 100 km in horizontal and a few hundred meters in vertical direction) to be transported
by realistic convective systems. Thus, they are more suitable to describe large-scale convective outflow
rather than the convective towers which are well below their horizontal resolution. This fact
justifies to a certain extent our restriction to consider only deep convective events with

In this section, we describe the details of the CLaMS configuration for the simulations with extended tropospheric
transport (v2.0), show in which part of the atmosphere the CLaMS air parcels are affected by this extension,
and compare the respective AoA distributions.
We especially investigate the propagation of the

As for the reference simulation described in subsection

Zonal mean of mean age of air (AoA) for the reference simulation

List of CLaMS reference and control simulations with different configurations of mixing, unresolved convective updrafts,
and parameter

In addition to the REF configuration, we use two slightly different configurations:

Furthermore, both apparently different choices of

As a first step toward extended tropospheric transport (in the following denoted as control runs),
we decrease the advective time step of trajectories from 24 to 6 h and, to keep the intensity of the standard
CLaMS mixing scheme roughly constant, we also increase the Lyapunov exponent from

The next step is to add new tropospheric transport, i.e., tropospheric mixing (TROP_MIX) and
unresolved convective updrafts (UNRES_CONV). Before discussing these new contributions
we first show our results in Fig.

Here, the zonal mean distribution of AoA,
calculated relative to the Earth's surface for 1 day (19 August 2005),
is plotted for the three cases discussed above: REF (Fig.

It is easy to tag and count all air parcels in CLaMS which undergo additional tropospheric mixing and which
are lifted from the lower boundary to the middle and upper troposphere by the deep-convection scheme
introduced in the previous section. In Fig.

Note that CLaMS tropospheric mixing practically does not affect any air parcels in the stratosphere
(the zero line of the calculated fraction is well below the tropopause, not shown).
Note also that numbers of air parcels affected by the deep convection scheme are
smaller than 10 % with highest levels (around 360 K) during JJA, mainly related
to the Asian summer monsoon (not shown). Furthermore, both tropospheric mixing and the deep convection
transport show some seasonality like

The atmospheric mixing ratios of

In CLaMS,

The zonal means of

Upward propagation of the

Now, the

Here, we use the zonally and monthly averaged time evolution of these observations between 2005 and
2008 interpolated at a latitude–altitude grid with 10

In particular, the comparison of the seasonal cycle and trend at 15

There is a clear improvement in the representation of the

For this purpose, we discuss in Fig.

Annual and zonal mean of AoA (for 2007, in years) as derived from the reference simulation
REF_0.7

As a reference distribution we use the AoA of the REF_0.7 case (shown in the Fig.

As expected, the air below the tropical tropopause becomes younger by up to 6 months if the additional tropospheric
transport is included (Fig.

Implementation of mixing in Lagrangian transport models is still an important issue in the ongoing
scientific discussion.
Here, we follow the idea of using numerical diffusion to parametrize physical mixing which
was first proposed and implemented in connection with the Chemical Lagrangian Model of the
Stratosphere (CLaMS). In particular, we extend this idea to the troposphere where vertical stability
is much smaller if compared with the stratosphere for which CLaMS was originally developed.
By using the lapse rates of the dry and moist potential temperature mainly defining the squares
of the dry and moist Brunt–Väisälä frequencies

The implementation of both processes improves CLaMS performance measured here
in terms of the quality of the simulated

By including other species like CO, ozone,

CLaMS v2.0 discussed in this paper is available at the GitLab server:

The CONTRAIL

Vertical instability is strongly related to the concept of buoyancy.
We now condense some textbook knowledge and start from the Boussinesq approximation
of the vertical momentum equation by taking into account only buoyancy effects
(e.g., see

The right-hand side of Eq. (

The equivalent potential temperature

Now we generalize this concept to the atmosphere containing water vapor,
i.e., to the moist atmosphere (e.g., see

Using the same type of arguments as for the dry atmosphere, we also
quantify the vertical instability of the moist atmosphere in terms of the lapse rate of the equivalent potential
temperature

For comparison, we also use the known concept of convective available
potential energy (CAPE), which can be understood as a different measure of the
unstable buoyancy

CAPE (red) versus stability-based (cyan) measure of potential convective uplift,

Then, CAPE is defined as the following integral (in J kg

Whereas

In this paper, we use the condition

To derive Eq. (

Using the entropy definition of the potential temperature

To estimate the influence of our convection parametrization on the mass budget, we
calculate the zonally resolved (i.e., per latitude bin

Figure

Annually averaged and zonally resolved updrafts due to parametrized convection (

PK and MT conceived most of the presented ideas and performed the numerical simulations. PK wrote the paper with support from FP. MD helped to use the CONTRAIL and the CarbonTracker data. MR supervised the findings of this work.

The authors declare that they have no conflict of interest.

The European Centre for Medium-Range Weather Forecasts (ECMWF) provided meteorological analysis for this study. We thank the CONTRAIL team, in particular Toshinobu Machida and Yousuke Sawa, for helping us to use this data set. The authors sincerely thank Andy Jacobson and Pieter Tans from NOAA for support related to the CarbonTracker data. We also thank Rolf Müller and Michael Volk for helpful discussions. We are thankful to Marta Abalos for providing us with the WACCM e90 climatology. Excellent programming support was provided by Nicole Thomas. Jens-Uwe Grooß helped us to make the source code available at the GitLab server. Finally, we would like to thank all reviewers for their insightful and probably very time-consuming reviews, as these comments led to an improvement of the work. We especially thank Ingo Wohltmann for his important comment related to the mass budget violation if unresolved convective updrafts are considered. This research was supported by the German Helmholtz Association within the Helmholtz-CAS Joint Research Group (JRG) “Climatological impact of increasing anthropogenic emissions over Asia”.

The article processing charges for this open-access publication were covered by a Research Centre of the Helmholtz Association.

This paper was edited by Volker Grewe and reviewed by two anonymous referees.