GMDGeoscientific Model DevelopmentGMDGeosci. Model Dev.1991-9603Copernicus PublicationsGöttingen, Germany10.5194/gmd-9-789-2016IL-GLOBO (1.0) – development and verification of the moist convection moduleRossiDanieleMauriziAlbertoa.maurizi@isac.cnr.itFantiniMauriziohttps://orcid.org/0000-0003-0962-9190Institute of Atmospheric Sciences and Climate, National Research Council, CNR-ISAC, Bologna, ItalyAlberto Maurizi (a.maurizi@isac.cnr.it)26February2016927897973August201528September201516February201619February2016This work is licensed under a Creative Commons Attribution 3.0 Unported License. To view a copy of this license, visit http://creativecommons.org/licenses/by/3.0/This article is available from https://gmd.copernicus.org/articles/9/789/2016/gmd-9-789-2016.htmlThe full text article is available as a PDF file from https://gmd.copernicus.org/articles/9/789/2016/gmd-9-789-2016.pdf
The development and verification of the convective module of IL-GLOBO, a
Lagrangian transport model coupled online with the Eulerian general
circulation model GLOBO, is described.
The online-coupling promotes the full consistency between the Eulerian and
the Lagrangian components of the model. The Lagrangian convective scheme is
based on the Kain–Fritsch convective parametrization used in GLOBO.
A transition probability matrix is computed using the fluxes provided by the
Eulerian KF parametrization. Then, the convective redistribution of
Lagrangian particles is implemented via a Monte Carlo scheme.
The formal derivation is described in details and, consistently with the
Eulerian module, includes the environmental flux in the transition
probability matrix to avoid splitting of the convection and subsidence
processes.
Consistency of the Lagrangian implementation with its Eulerian counterpart
is verified by computing environment fluxes from the transition probability
matrix and comparing them to those computed by the Eulerian module.
Assessment of the impact of the module is made for different latitudinal
belts, showing that the major impact is found in the Tropics, as expected.
Concerning vertical distribution, the major impact is observed in the
boundary layer at every latitude, while in the tropical area, the influence
extends to very high levels.
Introduction
Long-range transport of atmospheric tracers plays an important role in
several fields ranging from atmospheric composition and chemistry to climate
change, with applications spanning from air pollution to natural or
anthropogenic disaster management and assessment.
Lagrangian description is the natural framework for tracer dispersion
modelling, and the use of Lagrangian particle dispersion models (LPDM) for both
theory and application is very effective and widespread. In particular,
Lagrangian models are
used often to retrieve information about the sources contributing to the
concentration at a specific location (known as “backtrajectories”). The
consistent implementation of LPDM requires the careful consideration of all the
processes involved in the atmospheric dispersion.
Depending on the geographical area and season, the redistribution of tracers
released in the atmosphere can be largely affected by the vertical transport
due to moist convection events. In particular, convection is very efficient
in mixing the boundary layer with the free-troposphere air
contributing to the long-range
spread of local emissions.
Moist convection is widespread in the Earth's atmosphere where it displays a
wide range of space- and timescales in response to the variability of
environmental parameters, ranging from the sub-kilometre/tens-of-minutes of
individual cumuli to hundred-of-kilometre/several days of mesoscale convective
complexes see e.g..
For all the scales smaller than or close to the grid size of the numerical
models, explicit resolution is inadvisable, and numerical models resort to
parametrization schemes.
A discussion of the theoretical issues and field of application of the
different convective parametrizations is beyond the scope of this
introduction – the interested reader is referred to
and references therein. In this work, a slightly
modified hereinafter KF scheme is adopted,
which will be described briefly in Sect. .
For the turbulent diffusion processes (that are predominant in the boundary
layer), whose typical space- and timescales are small compared to the
resolution of a general circulation model, a well-founded theoretical framework
exists and allows for the formulation in terms of stochastic processes
. In contrast, mass-flux theories of moist convection do
not provide sufficient details to implement stochastic models. Therefore,
moist convection effects are simulated using particle redistribution mechanisms,
which reproduces the expected mass fluxes obtained from an Eulerian convective
scheme parametrization, usually via a Monte Carlo scheme
e.g..
While coupled chemistry and meteorology models (CCMMs) are now at the front
edge of research in atmospheric composition studies
, popular LPDMs are designed for offline usage
and need to reconstruct necessary quantities that are not included in the
normal output of meteorological models. In particular, off-line
recalculation of convective mass fluxes is needed, from quantities made
available from the meteorological (Eulerian) model such as temperature and
moisture, and is often performed with a mass-flux scheme different from the one
that produces the meteorological output see
e.g., possibly leading to dynamical
inconsistencies in the results.
To avoid this inconsistency, IL-GLOBO was designed as an
online-coupled model that makes use of the full availability of Eulerian fields.
In its first step of development, the vertical transport and dispersion of
tracers were the result of the vertical advection and diffusion only.
In the absence of a convective parametrization, explicit convection can occur,
and thus some vertical transport of tracers were present in the previous version
of the model. However, since the scales of convection are in the sub-kilometre range,
any explicit representation of it at coarser resolution is bound to
misrepresent most of those scales, and create updrafts that are incorrect in
location and strength. Therefore the inclusion of a moist convection Lagrangian
redistribution mechanism is essential to the completeness of the model. The
IL-GLOBO moist convection module is developed consistently with the modified KF
scheme adopted in GLOBO (see Sect. ).
With the online coupling this module benefits from the full availability of
all meteorological variables at every time step.
In this paper the development of the online-coupled convective module of
IL-GLOBO is presented and its features will be assessed
through some application examples. In Sect. the Eulerian
convective parametrization is presented while the implementation of the Lagrangian
scheme is described in Sect. 3 with emphasis on Eulerian consistency and
providing full details of the constructive procedure. Verification of the
scheme and some evaluation of the inclusion of convective effects in
IL-GLOBO are presented in Sect. 4.
The Kain–Fritsch scheme
A convective parametrization that makes explicit use of the vertical fluxes
of mass, the KF scheme, was adopted by the GLOBO
developers, and in the present work, for its ready availability, ease of
implementation and
widespread use by the meteorological research community.
The original formulation, and its successive evolution, were presented in a
series of papers to which the reader is referred for more details. Recent
presentations of its performance in the simulation of meteorological events
can be found e.g. in and
.
The scheme is based on a steady-state entraining–detraining plume model and
a closure based on release of convective available potential energy (CAPE).
Three streams of mass are present: updraft and downdraft of the convecting
ensemble, and a weak environmental flow (subsidence) that maintains the
balance of mass at each model level.
SkewT–logP thermodynamic diagrams for a deep tropical convective
episode, before (left panel) and after (right panel) the action of convection
as determined by the parametrization scheme: pressure on left axis in hPa,
temperature on right and top axes in ∘C. Middle panel: profiles of
vertical mass fluxes as computed by the convection scheme: updraft
(Fu, thick solid line), downdraft (Fd, thin solid
line), environmental subsidence (Fe, dashed) needed to maintain
the balance of mass at each level (see Fig. for
definitions). Vertical coordinate for the middle panel is pressure, with the
same scale indicated for left and right panels. Horizontal coordinate is
kg s-1 m-2 with arbitrary scale: the
flux per unit area depends on the area attributed to the convective ensemble
by the convection scheme. In this instance it is about 7 % of the grid
box. Also shown on the central axis are the locations of model levels.
Significant levels for the convection computation are labelled on the graph.
The air in the updraft source layer (USL) becomes saturated when raised to
the lifted condensation level (LCL), and is unstable when further pushed to
its level of free convection (LFC – at the same model level in this
instance). Vertical acceleration of the rising air parcel ceases at the level
of equilibrium temperature (LET) and vertical motion stops at cloud top. The
convective downdraft begins at the level of free sink (LFS) and extends down
to the ground.
The updraft is a detailed account of the thermodynamics of moist
air and entrainment–detrainment of moisture and condensate at every level
between cloud base and the cloud top. Briefly, mixtures of low-level air
are tested for instability. Once a lifted condensation level (LCL) is
identified, the parcel buoyancy at each upward level is computed, and an
estimate of the kinetic energy gained by latent heat release obtained. The,
as yet unspecified, upward mass flux is then fractionally increased/reduced
by entrainment/detrainment of environmental air based on a buoyancy-sorting
principle. The dilution of the originally unstable air with drier and
cooler air from the environment reduces its buoyancy, up to an equilibrium
level (LET) where the rising air has no more acceleration from thermodynamic
processes. Upward of the LET, the rising air is decelerated until the
remaining kinetic energy of the vertical
motion is reduced to zero, which defines the top of the cloud.
Downdrafts are generated by re-evaporation of water condensate expelled
by the rising motion. Environmental air is assumed to be
entrained uniformly into the downdraft in a layer around cloud base,
and detrained, again linearly in pressure, at lower levels. The
empirical evidence
for this structure is discussed at length in .
Only at this point are the dimensional mass fluxes determined by applying the
closure assumption that requires at least 90 % of the CAPE to be
consumed by the ensemble of convective clouds. This finally determines the
fraction of a grid box covered by the ensemble of clouds and the environmental
subsidence needed to maintain the balance of mass at each level.
The tendencies of thermodynamic quantities to be returned to the model
are spread over a “convective timescale” ΔTC, ranging from half
an hour to an hour, covered by several advective time steps Δt,
so that each model time step only receives a fraction of the convective
tendencies.
An example of the effect of the scheme on an unstable atmospheric profile is
shown in Fig. .
Lagrangian implementation of the moist convection effects
IL-GLOBO uses some of the quantities computed by the KF convective
parametrization (see Sect. ) to implement a Monte Carlo
scheme (KF-MC) for the particle displacement, in a way similar to other LPDMs
. All these schemes
compute the displacement probability matrix (DPM) between levels making use
of the entrainment and detrainment fluxes in updraft and downdraft.
Additionally, in IL-GLOBO the environment effects (subsidence), that result
from a mass balance, are directly included into the DPM, and therefore
implemented using the MC scheme, without the need of a posteriori
adjustment.
In the following, the same notation as in Fig. 1 of
is used where NLEV σ-hybrid grid
levels are indexed decreasing with height.
Schematic representation of fluxes involved in the KF scheme.
Uppercase F represent the fluxes between vertical levels (across level
boundaries) while lowercase f are the fluxes within a level that
represent the exchange of mass between environment (e) and updraft (u) or
downdraft (d), respectively.
In the Eulerian model component, every ΔTC (or, in terms of time
steps, every nC advective time step Δt), the KF scheme checks for
the conditions for the onset of convection and, if conditions are met,
determines the evolution of the grid column for the whole ΔTC.
Entrainment and detrainment fluxes in both updraft
(fuε, fuδ) and downdraft (fdε,
fdδ) for each level (see Fig. ),
from the ground to the cloud top, as computed by the KF scheme are made
available to the Lagrangian model. With reference to
Fig. , the following
relationships hold for fluxes at (f) and between (F) levels:
Fiu=Fi+1u+fiuε-fiuδ
for the updraft (u) and
Fi+1d=Fid+fidε-fidδ
for downdraft (d).
The probability for a particle to be entrained in an updraft at level i
is expressed by the product of the probability to be entrained from the
environment (fiuεΔt/mie) and the probability
that the particle resides in the environment (mie/mi), where mie
is the mass already present in the environment as opposed to the mass
flowing through, in the convective ensemble, and mi is the total mass of
the level i, giving
piuε=fiuεΔtmi.
The probability that a particle captured by the updraft is detrained can be
easily derived by rearranging Eq. () into
FiuFi+1u+fiuε+fiuδFi+1u+fiuε=1 .
Noticing that the two terms are both positive by definition, the above
relationship can be used to define the probability
piuδ=fiuδFi+1u+fiuε,
which is identically equal to 1 at the cloud top where
Fitopu=0. The denominator Fi+1u+fiuε of
Eq. () is the flow entering the updraft volume
(see Fig. ) at level i and that is available to
detrainment process. The mass entering the level i which is not detrained
must flow to the upper level satisfying the continuity for the updraft
(Eq. ). In terms of probability, this is
expressed by the complementary probability piuδ‾=1-piuδpiuδ‾=FiuFi+1u+fiuε
which, combined with Eq. (), gives back
Eq. () confirming the consistency of the above
definitions of the probability components.
Using the above definitions it is possible to build the full transition
probability matrix for the updraft fraction. The probability that a particle
moves due to the updraft motion from a level i to a level j<i is equal to
the probability that the particle is entrained at level i
(Eq. ) times the probability that it is detrained
at level j (Eq. ) times the probability that it
is not detrained between level i and j+1 included.
In formula:
pu(j|i)=piuεpjuδ∏k=ij+11-pkuδ.
For the downdraft transition probability pd, a similar relationship
holds.
The probabilities pu and pd represent the upper and lower triangular
components of the total convective transition probability matrix pc
whose diagonal is defined by
pc(i|i)=1-p1uε1-piuδ-pidε1-pidδ.
The mixing produced by the convective motion (updraft and downdraft) needs to
be balanced by the environment flux (subsidence) to conserve the mass. For
the Eulerian part this is granted by the environmental flux computed in the KF
scheme. In Lagrangian terms this is equivalent to maintaining a well-mixed
state where the redistribution of mass is applied,
and can be expressed in terms of DPM. This consistency
is obtained by modifying the transition probability matrix pc by
imposing zero net flux at the interface between two model levels.
At level i, the mass fluxes (assumed positive upward)
across the two level interfaces i (upper) and i+1 (lower) due to the sum
of updraft and downdraft motion, are expressed in terms of probability as
Fic=∑k<ipc(k|i)mi-pc(i|k)mk
and
Fi+1c=∑k>ipc(i|k)mk-pc(k|i)mi
respectively. Thus, the mass conservation reads
Fic+Fie=Fi+1c+Fi+1e,
where Fe is the environment mass flux
which is directed downward except in very peculiar cases
The very unlike case of upward Fe is accounted for
in the numerical code to avoid numerical inconsistencies.
.
With the additional boundary condition
FNLEV+1e=0,
the environment flux can be computed iteratively through
Eqs. ()–().
The effect of the environment flux at surface i+1 is to increase the
transition probability from i to i+1 while reducing the probability of
the “null transition” (particle remains in the same model level). This results in the modification of the elements
of the diagonal:
p(i|i)=pc(i|i)-Fi+1eΔtmi
and sub-diagonal:
p(i+1|i)=pc(i+1|i)+Fi+1eΔtmi.
The final DPM is then defined by
p(j|i)≡pc(j|i)
for j<i or j>i+1 and by Eqs. () and
() for j=i and j=i+1, respectively.
It is worth noting that p is an Eulerian quantity that can be viewed as
the linear operator acting on an initial concentration vector to give the
concentration distribution after the convection mixing. However, since p is
defined in terms of a finite time step Δt, it may become unstable (flux in one time
step comparable to or larger than the mass of the level).
In fact, KF use a reduced time step ΔtKF=ΔTC/nKF, with integer nKF, internally computed to
maintain linear stability of the numerical scheme.
Consistently, the same ΔtKF is used to compute the
transition probability that will be iterated nKF times using the
MC scheme.
In order to implement the MC scheme, it is convenient to compute
the cumulative transition probability matrix P as
Pj,i=∑k=NLEVjp(k|i).
The MC scheme is applied in grid columns affected by convection to the
particles that are below the cloud top by extracting a random number χ,
uniformly distributed between 0 and 1, and comparing its value to
Pj,i,j=NLEV,itop until a jf is found so that
χ<Pjf,i.
A position is then attributed to the particle within the arrival grid
cell using the same χ number to interpolate linearly between the grid
cell boundaries :
σp=σ(jf)+χ-Pjf-1,i/Pjf,i-Pjf-1,iΔσ.
The MC scheme is iterated nKF times to obtain the final position
after ΔTC. Then, as for the tendencies of thermodynamic quantities
in the Eulerian part, the total particle displacement is spread over the
nC advective time steps that cover the convective period.
Model verification
In order to identify the main features of the KF-MC scheme, to verify its
implementation and to assess its impact on dispersion, some numerical
experiments were performed.
A number of convective episodes were extracted from a model simulation
performed using a horizontal regular grid of 1200×832 cells of
0.3∘× 0.22∘, that corresponds to a resolution of about 23 km
at mid-latitudes in longitude, and a regular vertical grid of 50 points in the
σ-hybrid coordinate. The advective time step used was Δt=150 s.
The convective timescale is TC≃30 min, i.e. the KF scheme
is executed every nC=11 advective time steps.
Displacement probability matrix
An example selected in the tropical area around noon is shown in
Fig. . The central
part of the figure show the DPM for that specific event along with the
vertical profiles of entrainment (bottom) and detrainment (left) fluxes in
both updraft and downdraft. In this example the significant levels as
defined in Fig. are σcloud top=0.41,
σLET=0.47, σLFS=0.79,
σLCL=0.93 and the USL is a mixture 60 hPa thick based on
the ground.
The two most likely transitions are:
the particle stays within the starting grid cell (highest values are
found in the diagonal because most of the model grid cell is not influenced
by convection);
the particle is transferred in the cell just below, due to the
environment flux (high values in the matrix sub-diagonal).
The other transitions are directly caused by convective motion and are consistently
less likely, with probabilities in the range 10-2–10-5.
It is expected that finer model resolution
would increase the ratio between the volume involved in convection to the
total volume of some model columns.
Updrafts generate transitions with highest likelihood for displacements
from levels next to the ground to levels just below the cloud top,
while the downdraft transitions are permitted only
from levels between 0.8 and 0.9σ to levels between 0.9 and 1.0σ.
This reflects the hypotheses underlying the formulation of the KF
parametrization.
Example of Displacement Probability Matrix (DPM) and the fluxes
generated by the convection mechanism, as function of the vertical
σ-hybrid coordinate. Panel (a) displays the DPM with origins
of displacement in the abscissa and destination in the ordinate.
Bottom (b) and left (c) panels display entrainment and
detrainment fluxes, respectively, for both updraft (red) and downdraft
(blue).
Algorithm verification
In order to verify the consistency of the implementation, the distribution
of initially well mixed particles were verified after convection to be still
well mixed. This is performed in 1-D-like configuration by
selecting 12 convectively active grid columns, releasing 4×104 well-mixed particles in each and integrating the model for a full ΔTC.
It is found that the distribution after such integration remains well mixed
within the same error interval used in .
However, this only provides a test of the numerical implementation and not
of the theoretical formulation and correct calculation of pc. In
fact, in contrast to the formulation of a Lagrangian turbulent diffusion
model for which well mixing provides a necessary and sufficient condition
, the well-mixed state in the present scheme is
maintained by construction of the environmental flux, whether pc is
correct or not.
Therefore an independent verification is necessary. This is done by
comparing the environment fluxes computed using the DPM from
Eqs. (), () and () to
those provided by the KF scheme.
Such a verification, performed for a number of convective episodes, confirms
that within the roundoff error (10-7) Eulerian and Lagrangian KF fluxes are
the same.
Impact of KF-MC on dispersion
The impact of convection on the particle dispersion in a fully
3-D experiment is considered. The aim is to assess the
importance of the moist convection mechanism with respect to diffusion and
advection.
Simulations start on 11 March 2011. Particles are released and then dispersed
for 6 days, and their position is sampled every hour.
The source consists of Np≃7.4×105 pairs of particles, each pair
sharing the same initial position. Particles are released between
σ=1.0 and σ=0.9 proportionally to the average vertical density
profile, and homogeneously distributed in the horizontal within three zonal
areas: around the Equator, within the tropical area (-15∘, +15∘), and
at mid-latitudes in the Northern Hemisphere and (+30∘, +60∘) and
Southern Hemisphere (-30∘, -60∘).
For each emission area, two different simulations were performed with the
KF-MC switched on and off.
Values of relative and absolute dispersion are shown in
Fig. . Absolute dispersion is computed as
Δa2=12Np∑p=12Npxp-xp02,
where xp is a generic particle coordinate that can indicate both the
particle vertical position (in Fig. represented as the
height above the model surface) and the horizontal distance along the Earth
surface, and xp0 is the starting position of the same particle.
Relative dispersion is computed considering the ensemble of pair of particles
sharing the same initial position and is defined as
Σr2=1Np∑p=1Np〈xp1-xp22〉,
where xp1 and xp2 are the position of each particle of the pair.
Results of the experiments, reported in Fig. , show
that absolute dispersion is influenced by convection mainly at the Tropics,
where the convective activity is more intense and the tropopause higher.
Moreover, the effect is far more relevant on the vertical which is the
direction directly influenced by the scheme.
Concerning the relative dispersion, the moist convection scheme has a
relevant impact on both the vertical and horizontal directions. The effect
is important in all of the zonal areas but is still more pronounced at the
Tropics.
The larger impact on horizontal relative dispersion compared to the absolute
dispersion can be explained by considering that as particles separate due
to convection, they are captured by different horizontal structures that, in
turn, rapidly decorrelate the motion of the two particles of the pair.
Vertical absolute
dispersion (a), vertical relative dispersion (b),
horizontal absolute dispersion (c), horizontal relative
dispersion (d). Notice that panels (b) and (d)
share the same y axis with panels (a) and (c),
respectively. Continuous lines refer to experiments with the MC convection
scheme active, while the dashed lines mark experiments made without it. Line
colours indicate the tropical distribution (red), northern middle-latitude
distribution (green), southern middle-latitude (blue), respectively. Absolute
and relative dispersion are defined by Eqs. () and
().
Left: vertical concentration profiles (in arbitrary units),
as function of σ. Colours and line-types have the same meaning as in
Fig. . In addition, the top of the release region
(σ=0.9), is displayed as a bold solid line. Right: difference
map (with convection minus without convection) of vertically integrated
particle number at the end of the simulation for all the three emission
subdomains (initial emission area as labelled in the figure: north, Equator,
south). Details on the concentration normalizations for both panels can be
found in Sect. .
The effect on concentration is shown in Fig. , where the
final concentration is displayed for vertical (Fig. , left panel) with
and without moist convection scheme. For the horizontal
Fig. , right panel, a difference map is shown.
Particles were counted for intervals of equal size and normalized so that
the starting concentration between 0.9 and 1.0σ is around 1.
Figure , left panel shows that moist convection has an important effect
close to the surface in all the areas, with an enhanced effect at the
Tropics. In the free troposphere, the effect is almost negligible except for
the tropical area above σ=0.4 where the largest effect is observed.
It is worth noting that, in the tropical area, particles reach high
levels even in the simulation without convection although with a
concentration smaller by a factor of 2.
Since the diffusivity only acts between 0.8 and 1σ in the vast
majority of cases, the vertical transport of particles producing the high
concentration above σ=0.4 can be attributed mainly to vertical
advection that results from large-scale convergence with minor contribution
from horizontal advection and orographic effects.
Figure , right panel, displays the map of differences of the vertically
integrated number of particles between simulations with and without
Lagrangian convection scheme.
Particles are sampled for each 0.6∘× 0.43∘ column and the
difference is normalized with respect to the initial number of particles per
bin. For the case of release in the tropical area, it can be noted that areas
of strong depletion are surrounded by relatively larger areas where the
difference is weakly positive. The structure of convective updrafts (see
e.g. Fig. ) is such that most of the upward-moving
mass comes from the lowest levels of the atmosphere (below cloud base) and is
returned to the environment in the upper troposphere, in the strong outflow at
the top of the cloud, while areas of weak subsidence surround the updrafts.
Particles released in the extra-tropical regions (north and south)
display different qualitative behaviour showing smaller-scale features with respect to
those released at the Tropics, in agreement with the expected horizontal scales
of convective cells.
Conclusions
A Lagrangian transport scheme for moist convection is implemented online in
IL-GLOBO in parallel with the integration of the Eulerian model.
This gives the Lagrangian scheme direct access to all the prognostic
variables without any need for additional diagnostics and ensures full
consistency of the DPM with the parametrization scheme. As a
consequence, the Lagrangian and Eulerian descriptions of tracer
dispersion in the coupled model are equivalent, as is expected on
theoretical grounds.
This aspect differs from the approach of other models found in the literature. The
quantities used in those cases to advect and diffuse Lagrangian particles are
diagnosed from the meteorological thermodynamics profiles with
parametrizations that may differ from that of the meteorological model, making
the Eulerian–Lagrangian consistency hard to realize.
The consistency of the present scheme with the Eulerian quantities has
been verified in a number of offline 1-D tests, where the model is shown
to conserve the mass and reproduce the expected fluxes.
Global experiments with tracers released close to the surface at different
latitudes show that the effects of the MC-KM is strong and gives rise to
large departures from the non-convective version even at mid-latitudes.
Vertical distribution displays again a larger difference at the Tropics.
However, even with the KF-MC deactivated (but still activated in the
Eulerian part, so generating the “correct” dynamics), at the Tropics some
tracer is observed to reach very high altitudes. This is found to be a
combined effect of advection, both vertical and horizontal.
The next step of the IL-GLOBO development will be the validation of the
models against available data, for which appropriate data sets are scarce, as noted by e.g. .
Code availability
The numerical code of the IL-GLOBO vertical moist convection module
(Fortran 90) is released under the GPL and is available at the BOLCHEM
website (http://bolchem.isac.cnr.it/source_code.do).
The software is packed as a library using autoconf,
automake and libtool which allows for configuration and
installation in a variety of systems. The code is developed in a modular
way, permitting the easy improvement of physical and numerical schemes.
The GLOBO model is available upon the signature of an agreement with the
CNR-ISAC Dynamic Meteorology Group (contact:
p.malguzzi@isac.cnr.it).
Acknowledgements
The authors would like to thank Piero Malguzzi for making the GLOBO model
available and for making himself available for the explanation of the
finer points of the numerics.
The software used for the production of this paper (model development, model run, data analysis, graphics,
typesetting) is free software. The authors would like to thank
the whole free software community and, in particular, the Free
Software Foundation (http://www.fsf.org) and the Debian Project
(http://www.debian.org).
Edited by: O. Boucher
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