A simplified model of the atmospheric boundary layer (ABL)
of intermediate complexity between a bulk parameterization and a three-dimensional
atmospheric model is developed and integrated to the Nucleus for European Modelling of the Ocean (NEMO) general circulation model.
An objective in the derivation of such a simplified model, called ABL1d, is
to reach an apt representation in ocean-only numerical simulations of some of the
key processes associated with air–sea interactions at the characteristic scales of
the oceanic mesoscale. In this paper we describe the formulation of the
ABL1d model and the strategy to constrain this model with large-scale
atmospheric data available from reanalysis or real-time forecasts. A particular
emphasis is on the appropriate choice and calibration of a turbulent closure scheme
for the atmospheric boundary layer. This is a key ingredient to properly represent
the air–sea interaction processes of interest. We also provide a detailed description
of the NEMO-ABL1d coupling infrastructure and its computational efficiency.
The resulting simplified model is then tested for several boundary-layer regimes
relevant to either ocean–atmosphere or sea-ice–atmosphere coupling. The coupled
system is also tested with a realistic

Owing to advances in computational power, global oceanic models used for research or
operational purposes are now configured with increasingly higher horizontal and vertical
resolution, thus resolving the baroclinic deformation radius in the tropics
(e.g.,

Historically, oceanic general circulation models (OGCMs) were forced by
specified wind stress and thermal boundary conditions (from observations or
reanalysis) independent from the oceanic state, thus often leading to important
drifts in model sea surface properties. To minimize such drifts, a flux correction
in the form of a restoration of sea-surface temperature and salinity toward climatological
values can be added

An increasing number of studies based either on observational studies and/or on air–sea
coupled simulations have unambiguously shown the existence of air–sea interactions at
oceanic mesoscales
(e.g.,

In the ASL coupling strategy the pressure adjustment mechanism is absent, and only a
small fraction of the downward momentum mixing mechanism is accounted for through the
modification of the surface drag coefficient depending on the ASL stability

The various aspects discussed so far suggest that a relevant coupling at the characteristic
scales of the oceanic mesoscales requires nearly the same horizontal resolution in the
ocean and the atmosphere (since the atmosphere must “see” oceanic eddies and fronts)
as well as an atmospheric component more complete than a simple ASL parameterization to
estimate air–sea fluxes. This assessment raises numerous questions on current practices
to force oceanic models across all scales

This remark is supported by the
conclusions of the CLIVAR Working Group on Model Development following the Kiel meeting
in April 2014:

The objective of the present study is to introduce a simplified model of the MABL
of intermediate complexity between a bulk parameterization and a full three-dimensional
atmospheric model and to describe its integration to the Nucleus for European Modelling
of the Ocean (NEMO) general circulation model

In this section we first provide some basic elements on model reduction
to motivate our approach and mention possible alternatives
(Sect.

Global oceanic models can be run at higher resolution than global atmospheric models
because of their affordable computational cost. From an oceanic perspective, we generally
simulate at high resolution (in space and time) ocean fields

Instead of directly using

The formulation of the ABL1d model is derived under the following assumptions:
(i) horizontal homogeneity (i.e.,

For the sake of consistency, it is preferable to use a bulk formulation
as close as possible to the one used to compute the three-dimensional large-scale
atmospheric data

This subsection describes the turbulence scheme used to compute
the eddy diffusivity for momentum and scalars. Those eddy diffusivities
are responsible for a vertical mixing of atmospheric variables due to
turbulent processes. The turbulence scheme we have implemented in
our ABL1d model is very similar to the so-called CBR-1d scheme of

Set of turbulence scheme constants from

The Dirichlet boundary condition for TKE applied
at the top

The minimum value for

The value of

Our current implementation of boundary layer subgrid processes is an
eddy-diffusivity approach which does not include any explicit representation
of boundary-layer convective structures. This could be done via a mass-flux
representation

As mentioned earlier, the ABL1d model (

Beyond the particular values of

When the model is forced by the large-scale pressure gradient (or the geostrophic winds),
the parameter

We have introduced so far the continuous formulation of the
ABL1d model. In this section we describe the discretization
methods used and how this model is included in the NEMO modeling
framework. In particular, the discretization of the Coriolis term
and of the TKE Eq. (

Vertical grid variable arrangements and important notations.

Since in our implementation the horizontal velocity components are collocated,
the discretization of the Coriolis term is straightforward and is energetically neutral.
In the event the ABL1d is integrated with a time step much larger than the oceanic
time step, specific care must be given to the stability of the Coriolis term time stepping. A semi-implicit scheme with weighting parameter

In Sect.

The TKE equation is discretized
using a backward Euler scheme in time with a linearization of the dissipation term

Another challenging task when implementing a TKE scheme is the discretization of the
mixing lengths. As mentioned earlier, four different discretizations of

In the following we provide the continuous form of the various ways
to compute

The performance of those four length scales for various physical flows
is discussed in Sect.

For the practical implementation of the ABL coupling strategy within a global
oceanic model, a proper coupling method is required for stability and consistency
purposes

Particular care has also been given to the compatibility between the ABL1d model
and

Run the ABL1d model over the whole ABL for each
category

Run a single ABL1d model with a category-averaged surface flux.
In the current version of NEMO

The second option has been
preferred because it is much easier to implement and more computationally efficient. It amounts
to consider an ice surface temperature averaged over all categories

compute surface fluxes over ice and ocean and integrate the ABL1d model for given values

compute the dynamics of sea ice,

update

distribute the fluxes over each ice category considering the updated values

compute the thermo-dynamics of sea ice.

As described in

The ABL1d model can be run in standalone mode (coupled or not with sea ice) with prescribed oceanic surface fields.

The ABL1d model can be run in detached mode; i.e., the

Schematic representation of the ASL forcing strategy (left) and ABL coupling strategy (right) in terms of code organization and required external data. The

An other capability implemented within the NEMO modeling framework
is the possibility to interpolate forcing fields on the fly. This is particularly useful
for the ABL coupling strategy since three-dimensional atmospheric data must be interpolated
on the ABL1d computational grid. As the current implementation of the on-the-fly
interpolation only works in the horizontal, the vertical interpolation of large-scale
atmospheric data on the ABL1d vertical grid is done offline. Nevertheless
it means that the size of input data compared to an ASL forcing strategy is

Description of the idealized experiments performed in Sect.

To check the relevance of our ABL1d model for idealized
atmospheric situations typical of the atmospheric boundary layer
over water or sea ice, we performed a set of single-column experiments.
Each of those experiments are evaluated with benchmark large eddy
simulations (LESs). Moreover, we use standardized test cases from the
literature to allow our results to be cross-compared with other
well-established ABL schemes. In the following we consider a neutrally
stratified (Sect.

Results obtained for the neutral boundary-layer
case of

We first propose to investigate the simulation of a neutrally stratified atmosphere
analogous to a classical turbulent Ekman layer. The selected case is based on
the setup described in

However, we did not find significant differences
in numerical solutions when using the following initial conditions:

The best agreement is obtained when using the
CCH02 constants along with

The results obtained for

All simulations with the CCH02 set of parameters show reasonable results.

Results obtained for the stably stratified boundary-layer
case of

Within the Global Energy and Water Exchanges (GEWEX) atmospheric boundary
layer study (GABLS), idealized cases for stable surface boundary
layers have been investigated

The main outcomes are as follows:

The CCH02 set of parameters provides results of better quality than the CBR00 constants. For the sake of simplicity, we will retain only the CCH02 parameters for the numerical results shown in the remainder.

The buoyancy- and vertical-shear-based mixing lengths

An idealized experiment particularly relevant for the coupling of the MABL
with mesoscale oceanic eddies (and potentially submesoscale fronts) was initially suggested by

The velocities are systematically initialized with geostrophic winds.
All simulations are run for

Zonal

Zonal

For this configuration, results will be mostly evaluated in terms of

The main outcomes are as follows:

In the frontal region the effect of horizontal advection is predominant and the ABL1d model cannot reproduce the horizontal lag seen in the reference solution when passing over the front.

The ABL1d model reproduces the downward momentum mixing mechanism correctly.
The best results are obtained with the buoyancy-based

The

Although relevant for the present study this 2D

2D time vs. height sections representing the temporal evolution of the
zonal

Temporal evolution of the zonal

An alternative to the

The main outcomes are as follows:

The response of the ABL1d model to evolving oceanic conditions is not local in time (it shows a temporal lag).

The good representation of the downward momentum mixing process is not sensitive to the bulk formulation.

Adding a relaxation term toward large-scale data does not deteriorate the realism of the solutions significantly.

Based on the results reported in this section, the best balance between
efficiency and physical relevance is obtained when using the parameter
values from CCH02 and the modified

Using atmosphere-only experiments, we have been focused so far on the good
representation of the downward momentum mixing mechanism and of the stable
boundary layers typical of areas covered with sea ice. In the following we
check that those two aspects are still adequately represented in a realistic
coupled NEMO-ABL1d simulation. This simulation will also be used
to look at the wind–current interaction, which was left aside so far.
We performed a

We use here a global ORCA025 configuration at a

Name list parameters in the NEMO(v4.0) to set in the name list section

In this section, we evaluate the ABL coupling strategy in a realistic context for a set
of relevant metrics. The objective is not to conduct a thorough physical analysis
of the numerical results but to illustrate the potential of the ABL coupling strategy
and its proper implementation in NEMO. To evaluate our numerical results, we use
standard metrics from the literature to quantify the wind–SST (a.k.a. thermal feedback
effect), wind–currents (a.k.a. current feedback effect), and MABL–sea-ice couplings

To quantify the surface wind response to SST, we show in Fig.

Other processes of interest are those related to the coupling between oceanic
surface currents, wind stress, and wind. Such coupling is responsible for a dampening
of the eddy mesoscale activity in the ocean. In

Yearly average of sea-ice cover (contours) and atmospheric
boundary layer height (shaded) over the antarctic

The last illustration of our implementation presented in this section is the
coupling of ABL1d with sea ice. As described in Sect.

A simplified atmospheric boundary layer (ABL) model has been
developed and integrated to an oceanic model. This development is made with
the objective to improve the representation of air–sea interactions in eddying
oceanic models compared to the standard forcing strategy where the

Now that an adequate computational framework and an efficient
turbulent scheme that can be operated for a reasonable computational
overhead have been developed, the next step is to
investigate the relevance of the single-column representation of
the ABL selected for the present paper. Indeed, several studies have
already shown that momentum vertical turbulent mixing, pressure gradient,
Coriolis, and nonlinear advection are all important to the momentum balance
in the marine atmospheric boundary layer at the vicinity of oceanic fronts
(see for example

Several ways to improve the methodology presented here are currently
under investigation. At a practical level, ways to lower the computational
overhead due to I/O operations will be investigated using the parallel
I/O capabilities provided by the XIOS library which is currently used in NEMO
only for outputs. At a more fundamental level, the continuous formulation of the
ABL1d model will be completed to improve the representation of the
momentum balance by integrating the effect of horizontal advection and
fine-scale pressure gradients. Increasing the complexity of the model should
allow the impact of the nudging term on the ABL solutions to be lowered.
In the event our approach turns out to be physically sound for a reasonable
complexity it could be useful not only for offline oceanic simulations but
also in coupled simulations to downscale the information from a low-resolution
atmospheric component to a high-resolution oceanic component. A standalone ABL
model of intermediate complexity could also play a role in coupled data assimilation
where the current practice is generally to assimilate data separately in the ocean
and the atmosphere, ignoring the air–sea interactions, which results in inconsistencies
at the air–sea interface in the initial conditions, causing initial shocks in the
coupled forecasts

In this appendix, following the methodology of

The similarity theory for the ASL in the neutral case is such that

We thus have two relations (

Under this assumption, combining Eqs. (

The expression of

Considering that

The ABL1d model is discretized on fixed in time and space
geopotential levels while the IFS model uses a pressure-based sigma
coordinate. A first step is to recover the altitude associated with
each sigma level. The pressure

Altitude

Because of the IFS numerical formulation and of the post-processing of output data,
the solutions sometimes contain high-frequency oscillations at the
vicinity of the land-sea interface. This problem is further compounded
when the nearshore topography is steep. The atmospheric fields over water
thus need to be smoothed horizontally to specifically remove the

Atmospheric surface pressure horizontal gradients in

The last aspect of the pre-processing of atmospheric data we would
like to discuss is the computation of the large-scale pressure
gradient (or equivalently of the geostrophic wind components)
The objective is to estimate the following terms:

Assuming a generalized vertical coordinate

compute

compute horizontal gradients

compute horizontal gradients

compute

finalize (we get a minus sign in

In the following we describe the discrete algorithms used to provide
the mixing lengths

The

By construction such mixing lengths are bounded by the distance
to the bottom and the top of the computational domain and revert
to the

As soon as

The standard NEMO algorithm

Recently,

This mixing length will be referred to as

For the sake of computational efficiency, we have derived a local
version of the

To finalize our description of the implementation of the simplified atmospheric boundary layer model in NEMO, we assess in this appendix the computational efficiency of our
approach. We compare the performance of two simulations: one with a coupling
with the ABL1d model (with

We first show in Fig.

Elapsed time for each time step of a

Report of the elapsed time and CPU time
in different sections of the NEMO (v4.0) code for the ASL forcing strategy
(left portion of the table) and the ABL coupling strategy (right portion of the table).
The timing is averaged on all processors.
The right-most column provides a quick description of the task handled by the corresponding section.
On top of the timing in seconds the percentage of the total CPU and elapsed time associated
with each section is reported in parentheses. The computational overhead associated with the ABL coupling strategy can be estimated from the

The changes to the NEMO code have been made on the
standard NEMO code (release 4.0). The code can be downloaded from the NEMO website (

FL wrote the paper with the help of all the coauthors. FL, GS, and GM designed and developed a preliminary version of the ABL1d model within the NEMO 3.6 stable version. This original code was then ported to NEMO release 4.0. JLR and HG provided inputs in the design of the TKE closure scheme and of the numerical experiments. FL carried out the idealized numerical experiments, GS the realistic experiments, and JLR the MesoNH simulations.

The authors declare that they have no conflict of interest.

We thank Anton Beljaars and one anonymous reviewer whose efforts helped to improve earlier versions of this paper. We also thank Pascal Marquet and Sébastien Masson for useful discussions.

Florian Lemarié and Jean-Luc Redelsperger also acknowledge the support by Mercator-Ocean and the Copernicus Marine Environment Monitoring Service (CMEMS) through contract 22-GLO-HR – Lot 2 (High-resolution ocean, waves, atmosphere interaction).

This research has been supported by the H2020 European Institute of Innovation and Technology (IMMERSE (grant no. 821926)).

This paper was edited by Christina McCluskey and reviewed by Anton Beljaars and one anonymous referee.