We have extended ATTILA (Atmospheric Tracer Transport in a LAgrangian model),
a Lagrangian tracer transport scheme, which is online coupled to the global
ECHAM/MESSy Atmospheric Chemistry (EMAC) model, with a combination of newly
developed and modified physical routines and new diagnostic and
infrastructure submodels. The new physical routines comprise a
parameterisation for Lagrangian convection, a formulation of diabatic
vertical velocity, and the new grid-point submodel LGTMIX to calculate the
mixing of compounds in Lagrangian representation. The new infrastructure
routines simplify the transformation between grid-point (GP) and Lagrangian
(LG) space in a parallel computing environment. The new submodel LGVFLUX is a
useful diagnostic tool to calculate online vertical mass fluxes through
horizontal surfaces. The submodel DRADON was extended to account for
emissions and changes of
Due to the increasing demand for including interactive tracers in climate
simulations it is becoming necessary to use global models which meet the
needs of a fast and exact tracer transport scheme. Commonly used methods to
describe large-scale transport in a general circulation model of the
atmosphere follow the Eulerian method. The Lagrangian (LG) method (i.e. from
the perspective of a fluid particle or parcel) is more frequently used
offline for trajectory studies in particle models like the global 3-D
chemistry transport model
ATTILA has already been used to study the advantage of Lagrangian water vapour
and cloud water transport on the model climate
In this study we introduce the extended and improved LG advection scheme
ATTILA, which has been parallelised,
modularised, and rewritten as a submodel for EMAC
First, the large-scale transport of trace species is
sensitive to the selected vertical velocity scheme
Second, convective transport is an
important fast vertical transport process for trace species in the
troposphere, and tracer distributions are sensitive to the convection
parameterisation
In the former (non-parallelised) version of ATTILA, convective tracer
tendencies were calculated in grid-point space and then transformed onto the
parcels
In Sect.
The ECHAM/MESSy Atmospheric Chemistry (EMAC) model is a numerical chemistry
and climate simulation system that includes submodels describing tropospheric
and middle atmosphere processes and their interaction with oceans, land, and
human influences
List of MESSy submodels used for the simulations in this study.
The following list gives an overview of the modified and newly developed
routines, which are presented in more detail in the following sections.
Modifications and extensions of physical processes included
additional subroutines for ATTILA to describe Lagrangian convection, a formulation of vertical movement of air parcels in ATTILA based on the
diabatic vertical velocity, a new submodel (LGTMIX) to calculate the mixing of compounds in Lagrangian
representation, and expansion of the submodel DRADON to account for the emission and decay of
New diagnostic and infrastructure submodels included
a new submodel for the infrastructure, such as for the calculation of random numbers in a
parallel environment, a sub-submodel that hosts the basic transformation routines needed in
ATTILA to convert variables from grid-point to Lagrangian representation and
vice versa (ATTILA_TOOLS), a new submodel that uses ATTILA_TOOLS to calculate the transformation
of user-specified variables between Lagrangian and grid-point space and vice
versa (LGGP) for the output, and a new submodel to diagnose the vertical fluxes through horizontal
surfaces (LGVFLUX).
ATTILA is a Lagrangian tracer transport scheme, now including LG convection,
which can optionally be selected to transport tracers in Lagrangian
representation in addition to the standard flux-form semi-Lagrangian (FFSL)
scheme
ATTILA runs online as a submodel within EMAC. A former version of ATTILA has
been described in detail by
In ATTILA the atmospheric mass is divided into single mass packets, which have
an equal air mass loading but no volume. The parcels are regarded as
centroids when they are advected with the wind field provided by the spectral
dynamical core of EMAC. The number of parcels within the atmosphere is only
limited by the available computational resources. A typical choice is an
average of three parcels per EMAC grid box, similar to what was documented by
To enable ATTILA in a distributed memory parallel environment (e.g. applying
a message-passing interface standard, MPI) we chose to follow a domain
cloning approach. Whereas the base model EMAC follows a classical horizontal
domain decomposition approach for distributed memory parallelisation, we
distribute the global number
During the simulation, each parcel keeps being bound to its initial task. Since all parcels on each task move around the entire globe with time, it is necessary to provide the required input variables to drive ATTILA (such as the wind velocity vector from EMAC) as global fields (i.e. by cloning of the global domain of these variables). The subroutines for data transpositions between parallel decomposed grid points and corresponding cloned global variables have been added to the MESSy infrastructure submodel TRANSFORM.
To facilitate the exchange of Lagrangian objects between Lagrangian-enabled
submodels as so-called
For tracers we further define two additional
Subroutines to transform and transpose variables between Lagrangian
ATTILA requires up to four series of pseudo-random numbers, one for the
boundary layer turbulence parameterisation (Sect. Only for uniformly distributed pseudo-random numbers, i.e.
without the Marsaglia polar method.
For the simulations analysed below, we used three uniformly distributed pseudo-random number series, all generated with the Mersenne Twister algorithm: for the boundary layer turbulence scheme, for the convection parameterisation, and for the initial placement of the Lagrangian parcels. The Monte Carlo diffusion was switched off.
For every time step (in our simulations:
In the vertical direction we may use either
The vertical velocity in this coordinate system is defined as the time
derivative of Eq. (
Every parcel located within the planetary boundary layer (PBL) is randomly displaced in the vertical direction within the corresponding grid cell. This stochastic mixing represents the boundary layer convective mixing process. The boundary layer height is calculated outside of ATTILA within the submodel TROPOP.
The LG convection scheme uses the mass fluxes of the standard grid-box
convection scheme in EMAC (submodel CONVECT) to calculate the convective
parcel movement. Therefore, we will first shortly introduce the convection
scheme of EMAC
Convection is parameterised by dividing a vertical column into an area of
updraft (superscript u), downdraft (superscript d), and an area of
compensating motion in the environment (superscript e). Convective transport
in EMAC is parameterised only in the vertical direction as a divergence of the
tracer mass fluxes
The change in mass fluxes with height is dependent on entrainment and
detrainment fluxes.
The corresponding tracer mass fluxes are as follows.
In our LG convection scheme air parcels can follow the updraft, downdraft, or
the compensating motion in the environment at a grid column with convection
within one time step. The forcing used for the Lagrangian convection scheme
is provided by the mass fluxes
If
If
The LG convection scheme strictly conserves local mass because for every
time step the number of parcels per grid box after convection equals the
number before convection (see
Mode of operation of Lagrangian convection in a vertical column.
Coloured circles are Lagrangian parcels;
The submodel LGGP (LaGrangian to Grid Point transformations) performs the transformation of variables from Lagrangian representation to grid-point representation or vice versa. The variables (channel objects) to be transformed are specified by the user in the &CPL namelist of the submodel.
Transformations of a variable from LG to GP use the information of
all parcels in the corresponding grid box and calculate
the sum of this variable over all parcels, the average of the variable over all parcels, the standard deviation of the variable over all parcels, or the average of the variable over all parcels in which the variable is
Grid boxes without parcels are either filled with a constant value (defined by
the user in the &CPL namelist) or with the value from a selected grid-point
variable (defined as channel object in the &CPL namelist).
The transformation from GP to LG distributes the variable onto all parcels in the respective grid box, either mass conserving (i.e. with equal share) or uniformly (i.e. with the same value of the GP variable). An example &CPL namelist is shown in the Supplement.
The submodel LGTMIX (LaGrangian Tracer MIXing) calculates the exchange of
tracer mass between Lagrangian parcels. Each Lagrangian parcel is described
by a mathematical point. Its tracer mixing ratio represents a mean over the
whole parcel. Turbulence in the ambient air leads to the mixing of air of
adjacent parcels. In order to avoid parcel-to-parcel communication, we
define a background mixing ratio
The user can specify in the LGTMIX &CPL namelist the mixing parameter
The submodel LGVFLUX is a useful tool to calculate online vertical
mass fluxes through horizontal surfaces. Mass fluxes through a
two-dimensional surface (e.g. isentropic surface, potential vorticity
iso-surface, pressure level) are calculated by analysing the movement of LG
particles through these surfaces (upward or downward) and summing over all
particles which cross the surface per unit time and area:
The submodel DRADON (diagnostic radon tracer in GP space (see Sect. 6.1 in
Further, for the transformation of emission fluxes in GP space into
Lagrangian tracer tendencies, the new routines of ATTILA_TOOLS (see
Sect.
Mean age of air (AoA) is a common metric to quantify the overall capabilities
of a global model to simulate stratospheric transport. It describes the
transit time of air parcels in the stratosphere
We performed two identical simulations with EMAC–ATTILA with respect to the
climate: one uses the kinematic vertical velocity to drive the Lagrangian
parcels, and the other uses the diabatic vertical velocity. The horizontal
velocity remains equal in both simulations. EMAC was operated in T42L47MA
resolution with 47 levels up to 0.01
ATTILA was initialised with GP for the results of the grid-point simulation (EMAC; note that these
are identical in both simulations), LG(diab) for the results of EMAC–ATTILA with diabatic vertical
velocity, and LG(kin) for the results of EMAC–ATTILA with kinematic vertical velocity.
The LG parcels are equipped with tracers with different properties.
SF SF
In the previous sections, we described a comprehensively updated version of
the LG tracer transport scheme ATTILA, including a new LG convection scheme
and the option to use a diabatic instead of the standard kinematic vertical
velocity.
In this section, we evaluate ATTILA by comparing the simulated
Zonal mean
Zonal mean
We use
Monthly mean
The NARE campaign took place in the vicinity of Nova Scotia and Brunswick,
Canada, in August 1993. Data were sampled over the ocean and over the
continent. We used the simulation data of a climatological mean August
(1960–2000) averaged over the region where the flights took place
(60–70
Vertical profiles of
Vertical profiles of
The calculation of AoA is performed in two different ways: by a so-called
clock tracer (a linear-in-time increasing tracer like SF
Zonal mean AoA at 20 km of height (
Mean AoA in the stratosphere is calculated from the SF
Zonal mean AoA (in years) from the SF
Zonal mean difference of AoA (LG(diab)–GP) from the SF
Normalised age spectra (tropics and poles) of the years 2006–2010
between 50 and 0.1
Normalised seasonal age spectrum from LG(diab) simulation of the
years 1990–2010 between 400 and 500 K at
50–70
AoA spectra are calculated directly from the clock transit times. These LG
clocks represent the actual time a parcel resides in the stratosphere after
it has crossed the tropopause level. However, these clocks do not “mix their
time” with other parcels. Therefore, the resulting spectrum might differ
from age spectra calculated from so-called AoA “clock tracers”
Zonal mean difference between LG(diab) with standard mixing of
the SF
Zonal mean difference between LG(diab) and LG(diab-nm) with no inter-parcel mixing. The stippled area is statistically significant to the 99 % level.
AoA is influenced by the amount of mixing between adjacent parcels.
Inter-parcel mixing can be regarded as a diffusion process leading to a
reduction of local AoA gradients. The effect of inter-parcel mixing makes
stratospheric air generally younger (Fig.
Zonal mean mass fluxes through the 380
Monthly net mass fluxes from the LG(diab) simulation through the 380 K isentrope for the northern and southern extratropics.
Stratosphere–troposphere exchange (STE) is characterised by a global-scale meridional circulation in which mass is transported upward in the
tropics and downward in the extratropics
Movement characteristic of parcels transported in the updraft in 1997. The vertical axis describes the start level of a parcel, and the horizontal axis describes the respective final updraft (end) level. Displayed are the respective numbers of parcels transported in the updraft, normalised with the maximum number.
The LG convective parcel movement depends on the calculated mass flux profile
(from convection). We analysed the movement of parcels during deep convective
events for the year 1997. The analysis of movement shows that within the
updraft the largest number of parcels leave the boundary layer and are
detrained into the free troposphere up to the tropopause (Fig.
Similar to Fig.
Similar to Fig.
In this study we described and evaluated the updated LG tracer transport
scheme ATTILA. ATTILA was extended with an LG convection scheme and a
formulation of diabatic vertical velocity. We implemented a submodel to
describe inter-parcel mixing, which has so far been set up with one parameter for the
troposphere and one for the stratosphere. Moreover, the new
submodel allows us to easily implement more physically sound mixing parameterisations.
New infrastructure submodels which simplify the transformation
between GP and LG space, the provision of random numbers in a parallel
environment, and diagnostic submodels were developed. We performed two
simulations from 1950 to 2010, both resulting in the same meteorological
sequence in GP. The simulations differ only with respect to the vertical
velocity used for the LG model: one with a diabatic LG(diab) and one with the
standard kinematic vertical velocity LG(kin). The annual cycle of the two LG
simulations of
In a next step, we plan to parameterise phase changes of water vapour due to convection and cloud development on the Lagrangian parcels. Then, ATTILA will allow us to study convective and large-scale water vapour transport consistently in convective regions and to assess the convective contribution to the stratospheric water vapour budget.
The Modular Earth Submodel System (MESSy) is
continuously further developed and applied by a consortium of institutions.
The usage of MESSy and access to the source code is licenced to all
affiliates of institutions which are members of the MESSy Consortium.
Institutions can become a member of the MESSy Consortium by signing the MESSy
Memorandum of Understanding. More information can be found on the MESSy
Consortium Website (
The supplement related to this article is available online at:
SB and PJ did the implementation, performed the simulations, analysed the results, and wrote the paper.
The authors declare that they have no conflict of interest.
The data on the annual cycle of
This paper was edited by Havala Pye and reviewed by two anonymous referees.