Introduction
Coupling different models that have been specifically developed to study only
limited aspects of the Earth's systems is becoming increasingly common due to
the need to simulate different environmental components – and their
interactions – simultaneously (Heavens et al., 2013). As regards numerical
oceanography, coupled hydrodynamic–biogeochemical models are widely used to
investigate and predict the physical, biogeochemical, and ecological properties of marine ecosystems across a
wide range of scales and provide useful tools that support environmental
management and policies.
The numerical implementation of a coupling framework between
3-D hydrodynamic models and biogeochemical models is not a trivial task
(Bruggeman and Bolding, 2014) because every model focuses on processes that
occur on different temporal and spatial scales and uses different numerical
parameterizations and schemes. Additionally, these models might be coded in
different languages or follow different coding “philosophies” with respect
to memory allocation, computational schemes, and code workflow. Furthermore,
hydrodynamic and biogeochemical models are often developed by different and
highly specialized scientific groups, whereas coupling requires
interdisciplinary expertise.
In recent decades, the increasing availability of significant computational
resources has allowed substantial improvements in hydrodynamic and
biogeochemical models in terms of both temporal and spatial resolution of the
simulations, which required new specific programming and coding expertise
(i.e. code optimization and parallel programming). In addition,
biogeochemical model complexity has increased through the inclusion of new
variables and processes (Robson, 2014), and model development has become a
cooperative and multidisciplinary task rather than an individual effort. A
large number of generic, open-source models are utilized by the scientific
community, and they can be customized to match the users' specific
applications. A non-exhaustive list of the main state-of-the-art,
hydrodynamic community models includes the MITgcm (Adcroft et al., 2016),
GOTM (Burchard et al., 2006), ROMS (Haidvogel et al., 2000), and NEMO (Madec,
2014), whereas examples of community biogeochemical models include the BFM
(Vichi et al., 2015), ERSEM (Butenschön et al., 2016), PISCES (Aumont et
al., 2015), and ERGOM (Neumann, 2000).
Hydrodynamic and biogeochemical models can be coupled by merging their codes
into a single larger new code, in which the original parts are intertwined.
In this case, biological models are inserted into the workflow of the
existing hydrodynamic model code (Burchard et al., 2006; Follows et al.,
2006) because, in general, hydrodynamic models have already been developed to
solve the partial differential equation of tracers and provide the coding
infrastructure to handle the spatial–temporal properties of the simulations
(i.e. bathymetry, boundaries, computational domain discretization).
Alternatively, a modular approach can be adopted: each component preserves
its own peculiarities, the coupling is performed only on localized portions
of the code, and there are clear application programming interfaces (APIs).
The separation of the two coupled components facilitates the maintenance of
each code within its development community, avoids possible large efforts in
solving the language differences between models, and eliminates the need to
keep models up to date with respect to the parent model. As an example,
Bruggeman and Bolding (2014) proposed a set of programming interfaces (FABM)
that allows communication between different hydrodynamic and biogeochemical
models.
In this paper, we present a coupling scheme between the MITgcm hydrodynamic
model and the BFM biogeochemical model for ocean biogeochemical simulations.
The two models are widely used, as described in the next sections, and have
already been coupled with several other models. For example, the MITgcm has
already been coupled to low- (Parekh et al., 2005; Follows et al., 2006) or
intermediate-complexity (Hauck et al., 2013; Cossarini et al., 2015a)
biogeochemical models for a few specific applications and to a specific
high-complexity model (Dutkiewicz et al., 2009) to explore the theoretical
aspects of intraspecific competition in plankton communities. On the other
side, the BFM has already been coupled to POM (Polimene et al., 2006), NEMO
(Vichi and Masina, 2009; Epicoco et al., 2016), and the offline OGSTM, an
upgraded version of OPA (Lazzari et al., 2012). A direct coupling between
MITgcm and BFM has not been implemented yet. Thus, we developed a dedicated
online modular coupler linking them. The new coupler is open source, and
allows us to exploit the high potentiality of the two models, to preserve the
sustainability of the programming effort, and to handle the future evolution
of the two codes. Further, the online coupling of hydrodynamic and
biogeochemical models allows us to drive the biogeochemistry at the same
frequency of the hydrodynamic processes, avoiding the use of large files
where hydrodynamic variables are saved at high frequency. It also ensures the
use of consistent differential operators (advection and diffusion) for
hydrodynamic and biogeochemical variables, and would eventually provide a
framework to describe possible feedbacks from biogeochemistry to
hydrodynamics.
We demonstrate that the new online coupled model provides reliable results
when simulating different marine ecosystems by correctly reproducing the
interplay between physical, chemical, and biological processes and
components. The coupled model also runs with good computational performance
and preserves the numerical accuracy of the solution. We consider that the
MITgcm–BFM model represents a promising tool for investigating marine
biogeochemistry at different spatial and temporal scales.
This paper is organized as follows. After a brief presentation of the two
models (Sect. 2), we focus on the technical aspects of the coupling
algorithm. In the subsequent section (Sect. 3), we describe the testing of
the new coupled hydrodynamic–biogeochemical model against the idealized case
of a cyclonic circulation in a closed basin and against a real case study in
the central Mediterranean Sea. The paper closes with a discussion of the key
issues of the coupling and future perspectives. A manual of the new code
package is detailed in the Appendix.
Formulation of the hydrodynamic–biogeochemical coupling
A coupled hydrodynamic–biogeochemical model is composed of three main
elements: a hydrodynamic sub-model, which solves the governing equations for
oceanic flows; a tracer transport sub-model, which solves for the transport
(advection and diffusion) of biogeochemical variables (commonly called
tracers); and a biogeochemical sub-model, which describes the relationships
(i.e. biogeochemical reactions) among the biogeochemical variables.
Following the common practice in which the biological feedback on transport
is negligible, one can assume that changes in biogeochemical properties do
not affect the water velocity, density, or other physical properties;
therefore, modifying the standard equations that underpin hydrodynamic models
is unnecessary. We adopted such an assumption for this numerical coupling
framework; however, this coupler was developed, in principle, to also handle
biological feedbacks on hydrodynamics. The coupled model solves the set of
partial differential equations specified below:
dvHdt+fk×vH+1ρc∇Hp′=FH,εnhdwdt+gρ′ρc+1ρc∂p′∂z=εnhFV,∇H⋅vH+∂w∂z=0,ρ′=ρ(θ,S,p(z))-ρc,dθdt=Qθ,dSdt=QS,dCdt=QC+Rbio,PAR=PAR(Qsw,C),ddt=∂∂t+v⋅∇.
Momentum conservation equations, Eqs. (1)–(2), continuity and density
equations, Eqs. (3)–(4), and active-tracer equations (for potential
temperature θ and salinity S), Eqs. (5)–(6), are formulated
according to the semi-compressible Boussinesq approximation. In the
equations, vH=(u,v) is the horizontal component of
velocity, w is the vertical velocity, f is the Coriolis parameter,
ρc is a constant reference density, and p′ is the pressure
term. The right-hand side (RHS) terms in Eqs. (1), (2), (5), and (6)
correspond to the forcing and dissipation terms, including the diffusion,
which acts on the momentum (FH and FV in Eqs. 1–2)
and on the temperature and salinity (Qθ and QS in
Eqs. 5–6). Similarly, Eq. (7), which stands for a system of partial
differential equations of tracers (C), encompasses the forcing and
dissipation terms for biogeochemical tracers, QC, and the
biogeochemical reactions that occur in the sea, Rbio.
Equation (8) is an equation of state that calculates the modulation of irradiance
PAR (photosynthetic active radiation) with depth starting from
short-wave surface radiation fields (Qsw). The total derivative
accounts for the partial derivative in time and the advection term, which is
related to the flow field, Eq. (9).
By adopting a more explicit formulation and commonly used assumptions based
on scale analysis (see Crise et al., 1999), Eq. (7) can be rewritten as
follows:
∂C∂t=-v⋅∇(C)+∇H(KH∇H(C))+∂∂zKV∂C∂z+wbio∂C∂z+Rbio(θ,S,ρ,PAR,C).
The first three terms on the RHS of Eq. (10) represent the advection (first
term) and diffusion (second – horizontal – and third – vertical – terms)
of biogeochemical tracers, where KH and KV are the
horizontal and vertical diffusivities, respectively, which are considered
separately because they have different spatial scales. The remaining terms
describe the sinking processes that affect biological particles (fourth term)
and biogeochemical reactions (fifth term).
Within a coupled model, Eqs. (1)–(6) are solved by the hydrodynamic
sub-model, whereas Eq. (10) is solved partly by the transport sub-model,
which is usually embedded in the hydrodynamic code, and partly by the
biogeochemical sub-model. The other components, such as Eq. (8), the
biogeochemical tracers' forcing terms (QC, e.g. surface and
bottom boundary conditions), and the sinking terms, can be handled by either
the hydrodynamic or biogeochemical model, according to the specific processes
and the features of the codes.
A coupler is defined as the interface that transfers the hydrodynamic
information from Eqs. (1)–(6) to Eq. (10) and controls the communication
between the different terms of Eq. (10). In this study, the sub-models
coupled are the MITgcm (managing both hydrodynamics and transport) and BFM
(for the biogeochemistry) models, which are described in Sects. 2.2 and 2.3.
The algorithm used to construct the fully coupled system is detailed in
Sect. 2.4.
Nomenclature and units
Throughout the text, we used the following convention. In equations and text,
C refers to the concentration (mass per unit volume) of biogeochemical
model state variables, which are referred to as pTracer (passive
tracer) in the MITgcm nomenclature. As regards BFM, the chemical components
in the subscript are in blackboard style (C: carbon; N:
nitrogen; P: phosphorus; S: silica). The pieces of code
and the names of the routines and files are in typewriter font. Appendix B
reports a list of all symbols and variables used throughout the text.
MITgcm
The MITgcm (Massachusetts Institute of Technology general circulation model;
Marshall et al., 1997) is a 3-D, finite-volume, general circulation model
used by a broad community of researchers. It can be customized to create
different simulation set-ups by modifying its packages and parameters
accordingly (Adcroft et al., 2016) and it has already been successfully
applied to a wide range of case studies for the world's ocean at various
spatial and temporal scales. The code and documentation of the MITgcm are
under continuous development. The modular Fortran77 code is open source
(copyright ©2016 MITgcm Developers and Contributors), and it can
be downloaded from the MITgcm website (http://mitgcm.org/) as a TAR
file or using a CVS pserver. The most recent online documentation can be
found at http://mitgcm.org/public/r2_manual/latest/. The MITgcm, which
is designed to run on high-performance computing (HPC) platforms, can solve
fully non-hydrostatic and hydrostatic equations and can handle different
free-surface formulations. Subgrid-scale turbulence in both the horizontal
and vertical directions can be parameterized by using different types of
closure schemes with either constant or variable coefficients (e.g.
Gent–McWilliams, Redi, Leith, Smagorinsky, KPP, and GGL90). The MITgcm code
is composed of several packages, and, depending on the selected experiment,
the compiled packages can be enabled or disabled during the runtime by
specifying the flag use PACKAGENAME=.TRUE./.FALSE. in the
data.pkg input namelist. The MITgcm's implementation used in this
paper was based on the Release 1 – Checkpoint 65 k (April 2015) version of
the code. Among the different available customization options, we adopted the
fully implicit barotropic time stepping for the free surface, which is
unconditionally stable. The vertical diffusion and viscosity terms in the
horizontal momentum equations were treated implicitly in time and were solved
by using the Euler backward method. The terms that were evaluated explicitly
in time were discretized by using the third-order Adams–Bashforth method for
the momentum equations and the Euler forward-in-time method for the transport
equations.
A native transport sub-model for passive tracers (the Passive TRACERS –
PTRACERS – package; according to the MITgcm's jargon, a passive
tracer is a generic tracer that has no influence on the hydrodynamics – e.g.
by changing the density and/or viscosity) is included in the MITgcm code.
This sub-model solves the first three terms on the RHS of Eq. (10) (transport
of a generic passive tracer). This transport is calculated by adopting a
direct space–time discretization method for the advection–diffusion part of
the tracer equations and a non-linear, third-order advection scheme with a
Sweby flux limiter (Sweby, 1984) to avoid spurious oscillations in the model
output fields. When employing the direct space–time method and the
flux-limited schemes, the Euler forward time stepping is adopted rather than
Adams–Bashforth.
Because of the different length scales, horizontal and vertical turbulent
processes are treated separately and are solved by adopting a selected subset
of several available parameterizations: in this study, we chose a mixed
Leith–Smagorinsky scheme for the horizontal processes (second term on the
RHS of Eq. 10) and the K-profile parameterization (KPP, Large et al., 1994)
for the vertical processes (third term on the RHS of Eq. 10).
The packages that were enabled during compilation (#define
ALLOW_PACKAGENAME) were the standard geophysical fluid dynamics
packages of the MITgcm (“gfd”: MOM_COMMON,
MOM_FLUXFORM, MOM_VECINV, GENERIC_ADVDIFF,
DEBUG, MDSIO, RW, MONITOR), the oceanic
packages (“oceanic”: GMREDI and KPP), and our
specific selections (TIMEAVE, CAL, EXF,
OBCS, FLT, DIAGNOSTICS, PTRACERS, and
GCHEM), including the coupling and long time-stepping packages
(BFMCOUPLER and LONGSTEP), which are the core of this
peculiar implementation.
BFM model: scheme of the functional interactions among the variables
in the version that was implemented in Lazzari et al. (2012), Melaku Canu et
al. (2015), and Cossarini et al. (2015b). Variable names follow the BFM
convention (Vichi et al., 2015). The subscripts indicate the chemical
components (C: carbon; P: phosphorus; N:
nitrogen; S: silica; O: oxygen).
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This code was compiled onto a Linux cluster that was equipped with Intel Xeon
Ivy Bridge processors by using both the native GNU compiler (gfortran with
openmpi libraries) and the Intel compiler (ifort: Intel Composer XE 2013 SP1)
and by adopting the optimization levels -O3 and -O2,
respectively. Overall, the model performance increased by approximately
10 % when using the Intel compiler. The results in this paper were
obtained using the Intel compiler with the optimization set to -O2.
Further details on the custom model installation are available in the
MITgcm's online documentation.
BFM
The Biogeochemical Flux Model (BFM) is an open-source, modular Fortran90
numerical model that was designed to describe the dynamics of the major
biogeochemical processes that occur in marine ecosystems (Vichi et al.,
2015). The standard configuration of the BFM solves the cycles of carbon,
phosphorus, nitrogen, silica, and oxygen in the water-dissolved phase and in
the plankton, detritus, and benthic compartments. Plankton dynamics are
parameterized by considering a number of plankton functional groups, each
representing a class of taxa. The BFM's plankton functional groups are
subdivided into producers (phytoplankton), consumers (zooplankton), and
decomposers (bacteria). These broad functional classifications are further
partitioned into functional subgroups to create a planktonic food web (e.g.
diatoms, picophytoplankton, microzooplankton). The structure of the plankton
functional types is modular and can be adapted to specific needs. In fact,
the BFM's code is organized into several modules devoted to several plankton
function types: Phytodynamics (for the phytoplankton functional
types), Mesozoodynamics and Microzoodynamics (for the
zooplankton functional types), and PelBacDynamics (for bacteria).
The two modules OxygenReaerationDynamics and
PelChemDynamics for the oxygen and carbonate system dynamics,
respectively, complete the pelagic system (subroutine
PelagicSystemDynamics). The EcologyDynamics interface
routine manages the memory allocation of the biogeochemical state variables
and derivatives, and the external information that is required to calculate
the biological equations: temperature, salinity, presence of ice, wind,
position of the cell with respect to the surface or bottom, and atmospheric
CO2 partial pressure. The code and a full description of the model
equations and parameterizations are freely available at
http://bfm-community.eu.
For this application, we adopted version v2 (Lazzari et al., 2012, 2016;
Teruzzi et al., 2013; Melaku Canu et al., 2015; Cossarini et al., 2015b),
which can be downloaded upon request from the BFM consortium website
(http://BFM-consortium.eu) under the GNU GPL license. The current BFM
version uses a 0-D data structure for the biogeochemical state variables. The
present BFM includes four components (C, N,
P, and S); four phytoplankton groups; four zooplankton
groups; one group each of bacteria, detritus, labile, and semilabile organic
matter; and additional variables, such as dissolved oxygen and alkalinity
(Fig. 1). In addition, chlorophyll is solved as a prognostic variable
according to the formulation of Geider et al. (1997), and the carbonate
system is solved by using the OCMIP formulation (Melaku Canu et al., 2015;
Cossarini et al., 2015b).
The coupler
In this coupling scheme, we adopted a modular approach by considering the
high complexity of the two models that were employed. The size of the codes
according to the SLOCCount tool (Wheeler, 2015) is approximately 400 000
code lines for the MITgcm and approximately 20 000 for the BFM. The coupler
is a package that handles the interface (APIs) between the host code
(MITgcm) and the BFM to solve Eqs. (7)–(8) and to efficiently manage the
matrices that contain the variables and tendencies shared by the two models
and the flow of information among the different sub-model components.
The MITgcm–BFM coupling (Fig. 2) was achieved by upgrading a few routines of
the MITgcm GCHEM package (GeoCHEMistry, details in Appendix A),
which handles the evolution of tracers, and by developing an additional
package, BFMCOUPLER, which was specifically designed as the
interface with the BFM model. The BFM is called by the MITgcm as an external
library; therefore, the BFM was compiled separately using the same compiler
used for the MITgcm (additional details on the compilation options and
instructions are provided in Appendix A).
The BFMCOUPLER package (dashed box in Fig. 2) manages the
initialization and memory usage of the BFM. This package also calls the BFM
core routines and solves several processes that are not included in either
model. The interfaces among the different components of the coupled model
were designed so that the tracer transport sub-model (MITgcm
PTRACERS package) uses the u, v, and w components of the
velocity and the horizontal and vertical diffusivities (KH and
KV) from the hydrodynamic sub-model to compute the tendency due to
the transport (gTracertrsp). Furthermore, the transport sub-model
must consider the boundary conditions along the open boundaries of the model
domain OBCc and the surface fluxes, such as the mass transport
associated with the evaporation minus precipitation minus runoff term
EmPmRc.
Description of the MITgcm–BFM coupling and interfaces among the
different components of the coupled model.
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As an interface, the BFMCOUPLER manages the transfer of information
that is required by the BFM from both the hydrodynamic and transport
sub-models of the MITgcm, and provides the integration solver (a MITgcm
package) with the biogeochemical surface and bottom forcing and the
sink/source terms originating from the BFM (gTracerbio). The values
of the tracers are derived from the transport sub-model. Moreover, the
hydrodynamic sub-model supplies the temperature, salinity, and photosynthetic
active radiation (PAR) values as well as additional forcing parameters
(presence of ice, wind speed, and air partial pressure of CO2) and
information, such as the position of the specific grid cell within the water
column (surface, intermediate, or bottom), which activates specific processes
(e.g. surface air–sea gas transfer or bottom sediment fluxes). Then, the BFM
calculates the biological partial derivative of Eq. (10) (fourth term), and
the BFMCOUPLER returns this term to the time integration package,
which integrates the transport and biogeochemical derivative terms to solve
Eq. (10). Certain information used by the BFM, such as the PAR and wind
values, can be calculated directly from the internal variables of the
hydrodynamic sub-model (such as short-wave radiation (Qsw) or other
atmospheric fields) or managed from external sources.
Integration scheme, operator splitting, and <monospace>LONGSTEP</monospace> options
We considered several coupling strategies according to the MITgcm's code
structure (Fig. 3). Within each time step of the model integration, which is
coded in the FORWARD_STEP routine, the MITgcm solves the
hydrodynamic equations (Eqs. 1–6) through several routines:
DO_ATMOSPHERIC_PHYS, DO_OCEAN_PHYS, DYNAMICS,
TEMP_INTEGRATE, and SALT_INTEGRATE; further adjustments
for temperature and salinity (e.g. filters) are applied in
TRACERS_CORRECTION_STEP (Adcroft et al., 2016).
Workflow of the MITgcm FORWARD_STEP routine. The boxes
indicate the routines (darker colours denote dependency). The matrix of the
tracers' state variables (pTracer), the overall tendency of the
tracer (gTracer), and the tendency for the biogeochemistry only
(gchemTendency) are also specified. The blue boxes indicate
modifications to either the MITgcm code or the BFMCOUPLER routines, whereas
the green boxes indicate BFM routines. The pre-compilation options (#) and
omitted parts (…) are also shown.
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Different options can be used to solve the evolution of tracers (Eq. 10),
which can be controlled by the
gchem_separate_forcing pre-compilation option. When this option is false (#ifndef
in Fig. 3), a direct integration scheme is adopted; therefore, the transport
(gTracertrsp) and biogeochemical (gTracerbio)
tendencies of each tracer
are calculated by using the same (current) values of the physical and
biogeochemical variables:
Cn+1=Cn+gTracertrsp(Cn,vn)+gTracerbio(Cn,θn,Sn,FC)Δt,
where v, θ, S, and FC are the hydrodynamic
variables and the additional biogeochemical forcing and Δt is the
time discretization, which is the same adopted by the hydrodynamic sub-model.
The biogeochemical tendency, which is solved by calling the BFM through the
BFMCOUPLER_CALC_TENDENCY routine, is temporarily stored in the
gchemTendency matrix, which is then summed to the overall tracer
tendency, gTracer, in the PTRACER_APPLY_FORCING routine,
along with the tendency term from the evaporation minus precipitation minus
runoff effect (surfPtracers). The transport terms of the tracers
(which update the gTracer matrix) are subsequently calculated
within the PTRACER_INTEGRATE routine by several subroutines
(GAD_ADVECTION, GAD_CALC_RHS, IMPLDIFF, and
others) according to the options and numerical schemes selected in the
specific MITgcm simulation set-up. The TIMESTEP_TRACER routine
calculates the integration of Eq. (10) by providing a new state for the
tracers. However, when the MITgcm set-up is prescribed with an implicit
vertical diffusion scheme, an update of the state of tracers is solved within
the IMPLDIFF routine according to the specific parameterization of
the vertical diffusion (e.g. KPP, GGL90). Finally, if open boundary
conditions are prescribed in the MITgcm set-up, the
OBCS_APPLY_PTRACER routine applies the updated values of the
tracers at the boundaries. The calculation of the derivative of the transport
processes (gTracertrsp) involves several MITgcm packages
(GENERIC_ADVDIFF, PTRACERS, GCHEM, OBCS,
KPP, and EXF) and options (choice of the advection scheme,
viscosity and diffusivity coefficients, parameterization of surface
dilution/concentration of tracers from evaporation, precipitation, and
runoff), which are exhaustively described in the MITgcm documentation
(Adcroft et al., 2016).
For the second coupling option, an operator splitting scheme is selected when
gchem_separate_forcing is true (#ifdef). In this
case, the biogeochemical tendency (gTracerbio) is calculated after
the state of the tracers has been updated by the transport equation terms. An
intermediate value of the tracers, C̃n+1, is passed to
BFMCOUPLER_CALC_TENDENCY along with the values of the updated
hydrodynamic variables (Eq. 12).
C̃n+1=Cn+gTracertrsp(Cn,vn)ΔtCn+1=C̃n+1+gTracerbio(C̃n+1,θn+1,Sn+1,FC)Δt.
This option allows for the development of an integration scheme with
different time steps for the hydrodynamic and transport parts on one side and
for the biological processes on the other.
A third option is an operator splitting algorithm, which involves the MITgcm
LONGSTEP package (Adcroft et al., 2016) and adopts different time
steps for the hydrodynamic and transport–biogeochemical components, thus
increasing the computational performance of a coupled simulation. In
particular, the tracer time step is set as a multiple (LSn) of the main
(hydrodynamic) time step, Δttrc=LSn⋅Δt, whereas the terms v, θ, S, and FC in Eq. (11)
are replaced by suitable averages of the physical variables. The calculation
of the averages is controlled by the LS_when_to_sample parameter,
which defines the position within the code workflow in which the hydrodynamic
variables are sampled (longstep_average, Fig. 3) and biogeochemical
tracer tendencies are calculated (LONGSTEP_THERMODYNAMICS, Fig. 3).
To activate this option, the LONGSTEP package code must be modified
properly: the LONGSTEP_THERMODYNAMICS routine must be modified by
adding a call to the modified GCHEM_CALC_TENDENCY routine.
This third method is preferred over the previous one as a possible method of
decoupling the numerical biogeochemistry solution from the hydrodynamic
solution. We tested the model to verify the trade-off between the increase in
computational performance and the loss of accuracy in the model results as a
function of the extension of the time step for the tracer equations
(LSn; see Sect. 3.1.3).
BFMCOUPLER processes
The core of the present coupling scheme is the new
BFMCOUPLER_CALC_TENDENCY routine, which is called by
GCHEM_CALC_TENDENCY or by GCHEM_ FORCING_STEP. The
approach adopted in this coupling scheme is to loop in space and to call the
BFM as a subroutine to calculate the derivative terms of each biogeochemical
tracer for each computational grid point (gTracerbio in Fig. 2).
The derivatives of the chemical and biological processes are calculated by
the BFM model via an Euler forward scheme through the
BFM0D_ECOLOGY_DYNAMICS routine (a BFM routine) and stored in the
4-D MITgcm gchemTendency matrix. Additionally, the contributions of
other processes, which are not explicitly coded in the BFM, are solved within
BFMCOUPLER_CALC_TENDENCY, namely, the light penetration
formulation, the sinking of phytoplankton and detritus, and the exchange
processes in the surface and bottom layers of the water column.
In particular, the BFMCOUPLER package calculates the vertical
profile of PAR along the water column, starting from the surface PAR,
which is read from an external file or by using the short-wave radiation
field (Qsw), which is converted into PAR by a standard bulk
formula if the native MITgcm atmospheric forcing package EXF is
active (Britton and Dodd, 1976):
PARs=Qsw⋅conv⋅pfrac,
where PARs is the PAR at the sea surface, conv is a
conversion factor of
4.6 µEin m-2 s-1 (W m-2)-1, and pfrac is
the fraction of the radiation in the visible band, which equals 0.4. The
calculation of PAR along the water column, Eq. (14), is performed in the
cell centre according to the Lambert–Beer formulation for the light
exponential decay with depth and the shading of detritus and phytoplankton:
PARz=PARs⋅e-∫0z(Kext+∑jChljKpj+RC(3)KR)dz,
where Chlj is the chlorophyll concentration of the jth phytoplankton
functional type (PFT), RC(3) is the carbon concentration of the
detritus or optically active organic matter, and Kpj and KR are the corresponding extinction factors. Kext represents a
background value set constant and is equal to 0.035 m-1 (considering
pure water), or it can be read from an external file. In the latter case, the
external file contains maps of the background extinction factor, which can be
built a priori to incorporate the contributions of different unparameterized
processes (e.g. the pattern distribution of yellow substances).
BFMCOUPLER solves the sinking processes and is activated for the
phytoplankton groups and detritus
(RC,N,P(3) variables in Fig. 1):
∂C∂tbiosink=ws∂C∂z,
where ws is the sinking velocity (m s-1), which is provided
both as a constant value or as a diagnostic result produced by the BFM model
based on the nutrient stress conditions of the phytoplankton cells (Lazzari
et al., 2012). The equation is solved numerically based on an Euler forward
scheme.
A second module of BFMCOUPLER was designed to easily handle the
boundary conditions at the surface and bottom. At the surface, air deposition
can constitute an important source of nutrients in oligotrophic systems.
Furthermore, when the runoff and nutrient discharge from rivers cannot be
incorporated into the MITgcm OBCS package (as in Cossarini et al.,
2015a), incorporating these factors as external surface forcings may be
necessary (i.e. as localized runoff). Therefore, such contributions are
prescribed as additional terms in gchemTendency in the surface layer
by reading time-varying 2-D maps from external files:
∂C∂tbiosurf=fluxCsurf.
The coupled MITgcm–BFM model includes a simple parameterization of the
fluxes at the water–sediment interface, which includes the burial of
detritus (e.g. a net export flux from the ecosystem) and an incoming flux of
nutrients into the deepest cell of the water column. Burial is parameterized
as the first-order kinetics of the carbon (C), nitrogen
(N), and phosphorus (P) content in the detritus
(RC,N,P(3) variables), which is
exported out from the bottom grid cell:
∂RC,N,P(3)∂tbiobottom=-kburialRC,N,P(3).
In the same grid cell, the nutrient (for C equal to N(1), N(2) and
N(3) in Fig. 1) bottom fluxes are set either as a constant rate over the
entire domain or as time-varying 2-D maps that can be read from an external
file or provided by the benthic module of the BFM (which is foreseen in an
ongoing development of the model):
∂C∂tbiobottom=fluxCbottom.
The BFMCOUPLER involves the use of several external surface forcing
fields, such as the surface photosynthetic active radiation, background light
extinction factor, sediment fluxes, and partial pressure of atmospheric
carbon dioxide, which are used by the BFM to
calculate the air–sea CO2 exchanges. These fields are managed by the
BFMCOUPLER package through the BFMCOUPLER_FIELDS_LOAD
routine, which is a specifically modified replica of the EXTERNAL_FIELDS_LOAD
routine of the MITgcm (Adcroft et al., 2016). This reading of
external fields is controlled by two parameters: the timespan
(forcingCycle) and the frequency (forcingPeriod) of
external forcing, which are specified in the BFMCOUPLER namelist
(additional details in the Appendix).
Compilation and set-up
The MITgcm and BFM must be compiled with the same compiler. We tested the
code by using both the GNU and Intel compilers on several HPC platforms.
Here, we report the results obtained by running the model (compiled with
Intel) on a Linux cluster. The BFM is compiled as an independent library by
using the following option of the BFM makefile: mkmf -p $BFM_LIB,
and by configuring the config_BFM.sh compiling bash script with the
appropriate compilation options (modules, optimization, and compiler), which
are also used for the MITgcm compilation. Then, the build_option file for
generating the MITgcm makefile must be modified by adding the path to the BFM
compiled library and include files. Additional details are given in the
manual of the BFMCOUPLER package (Appendix A).
Discussion and conclusions
In this paper, we presented a coupling between two widely used models, the
MITgcm and BFM, and we showed the potential of the new coupled model. These
two models were developed by two different scientific communities that are
actively and constantly involved in improving the codes. When one model is
directly embedded in another, code developments might represent an issue
because of the constant and tedious work of keeping one code updated with
respect to the other. Therefore, the coupling in this paper was designed to
preserve the independence of the two models as much as possible. The number
of modifications that were required for the two original codes was limited,
and changes could be easily managed should each single model be upgraded. In
our solution, the MITgcm remained the host code, the BFM was compiled and
linked as an independent library, and the new BFMCOUPLER package
handled all the coupling procedures and concentrated all the coding effort.
The upgrades to the MITgcm enumerated less than 10 new code lines in a few
routines (in the GCHEM and LONGSTEP packages) and the list
of available diagnostics (in the DIAGNOSTIC package). On the BFM
side, several “include” files contained a list of newly added variables.
The order of the variables in the BFM's include files and in the MITgcm's
data.ptracer file must be consistent (see Appendix A). This feature is
important because the BFM (Vichi et al., 2015) can be customized in terms of
the number of state variables and processes, thus increasing the
flexibility of the new coupled model for a wider range of applications.
Despite the growth of computational resources, the efficiency of coupled
codes can still be an issue because of the large size of the computational
grids (Blom and Verwer, 2000). Domain decomposition and parallelization tools
are available in several coupling environments (e.g. FABM, Bruggeman and
Bolding, 2014; MESSy, Jöckel et al., 2008). Likewise, our coupling scheme
has been thought to fully exploit the parallelization efficiency of the
MITgcm (Marshall et al., 1997), and no additional coding effort (in terms of
parallelization) is required by the users.
Other biogeochemical models of various complexity have already been embedded
in the MITgcm (Dutkiewicz et al., 2009; Hauck et al., 2013; Cossarini et al.,
2015a). Nevertheless, the BFM in this new coupled model has a biological
complexity and a number of features (Lazzari et al., 2016) that increase the
attractiveness of the model for many marine applications.
The MITgcm–BFM coupling scheme was primarily designed by considering the
direct integration scheme because this framework has the highest level of
numerical accuracy. The use of the LONGSTEP option reformulated the
coupling as an operator splitting algorithm that allows for different time
steps for hydrodynamics and coupled transport–biogeochemistry at the cost of
accuracy. When using the LONGSTEP option, the results (Fig. 6 and
Table 2) show that the loss of accuracy remained negligible only for a
limited increase in the tracer time step. Furthermore, the coupling framework
could handle a separate solution of hydrodynamics and transport processes
from the biogeochemical processes through the use of the
gchem_separate_forcing option (Fig. 3). However, this approach
would require a wider modification of the GCHEM package to introduce
independent integration steps for the transport and biogeochemical parts of
the tracers. Then, a more detailed analysis of the sensitivity (e.g. similar
to what was proposed in Butenschön et al., 2012) of the biogeochemical
model's results to the different coupling schemes and time steps should be
performed for each specific application.
A direct integration scheme might be more appropriate for investigating the
feedback of the biogeochemistry on the hydrodynamics of the system. An
example is the calculation for the sinking of certain phytoplankton groups,
which is a physical 1-D process solved within BFMCOUPLER and related
to the sinking velocity calculated by the BFM. Furthermore, the shading
effect on light penetration caused by phytoplankton and other suspended
matter currently only affects the PAR vertical profile (Eq. 14). However,
this factor could be introduced as an extra term in the routine that
calculates seawater thermodynamics (in the SWFRAC and
EXTERNAL_FORCING routines). A new parameterization of the
penetration of solar radiation could be used to estimate the biological
effects on the seawater temperature, which might be an interesting issue in
highly productive areas, such as the northern Adriatic Sea and the coastal
strip along the Italian coast reached by the Western Adriatic Current (WAC).
A realistic simulation of light absorption with depth could reduce the model
errors when estimating temperature, which is affected by many other sources
of uncertainty originating from the surface forcing data, the heat flux bulk
formulation, the vertical resolution, and the parameterization of vertical
turbulent processes. The design of our coupler, which is characterized by the
sharing of biogeochemical variables and their tendencies in the host model's
memory structure, allows for the future implementation of the feedback
effects of biology on hydrodynamics.
Furthermore, the new coupling scheme was designed to foster development
towards a full Earth system modelling approach, in which a wide range of
processes among the Earth's spheres can be simulated online and the
interactions and feedback effects can be directly considered. For example,
the BFM has already been coupled with other ecosystem components (e.g. online
coupling with high-trophic-level model Ecopath with Ecosym, Akoglu et al.,
2015). Moreover, the parameterization of Eqs. (16) and (17) can be easily
substituted by a call to a benthic model function, which solves the processes
that occur in a single-layer sediment model and calculates the exchanges
between the pelagic environment and the sediment.
Similarly, the MITgcm has already been coupled with atmospheric models. For
example, the MITgcm has been coupled online with the RegCM atmospheric model
in the Mediterranean Sea region (Giorgi et al., 2006) using the OASIS
coupling framework (Artale et al., 2010). Therefore, our coupling scheme can
act as a link between atmosphere–hydrosphere models and biosphere models.
This coupler could be successfully used to study ocean–atmosphere
interactions, such as the effects of climate scenarios on high-trophic-level
ecosystem components or the feedback of ocean carbon pumps on the climate.
Finally, the results of the two test cases show that the new coupled model
provides a realistic representation of a wide range of marine processes from
costal to open-sea ecosystems, where the interplay of hydrodynamics and
biogeochemistry is crucial. The effects of river plumes, coastal upwelling,
and different vertical mixing regimes on phytoplankton dynamics were
reasonably reproduced by the model and found to be consistent with both
theoretical knowledge (Mann and Lazier, 2006) and published experimental
findings for the Mediterranean Sea.