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\title{Brief Article}
\author{The Author}
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\begin{document}
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\section{3.1 Numerical Modeling}

Model Description
{\vskip 12pt}

We use the ORCA2\_LIM\_PISCES configuration of the NEMO (Nucleus for European Modelling of the Ocean),
a global ocean modeling framework which is composed of an ocean model ORCA2
coupled to an ice model LIM3 and a biogeochemichal model PISCES
(Madec et al., 1999; Madec, 2008; http://www.nemo-ocean.eu/About-NEMO).

%% The "engines" provide numerical solutions of ocean, sea-ice, tracers and biochemistry
%% equations and their related physics (http://www.nemo-ocean.eu/About-NEMO).
%% It is intended to be a flexible tool for studying the ocean and its interactions with 
%% the others components of the earth climate system such as atmosphere, sea ice, and 
%% biogeochemical tracers over a wide range of space and time scales.
%% We intend to use the ORCA2\_LIM\_PISCES configuration of NEMO
%% consisting of ORCA2, LIM3, and PISCES.
{\vskip 12pt}
{\noindent Ocean model:}
{\vskip 12pt}

The ocean component  ORCA2 of the NEMO modeling frame work is a hydrostatic, primitive equation ocean general circulation model. ORCA2 is a finite difference OGCM with a free sea surface.
%% Prognostic variables are the three-dimensional velocity field, the sea surface height, 
%% the temperature and the salinity.
%% It is based on the ORCA tripolar grid with 2 deg horizontal resolution with climatological 
%% or interannual forcing. 
In the ORCA2\_LIM\_PISCES configuration, the model domain extends from 78S to 90N. 
The model uses a global tripolar orthogonal curvilinear grid with 2 deg zonal resolution,
and a meridional resolution varying from 0.5 deg at the equator to 2 deg cos(phi) south of 20S.

The horizontal grid features two points of convergence in the Northern Hemisphere, both situated
on continents to overcome the North Pole singularity found for geographical meshes, 
thus avoids singularity point inside the computational domain [Madec and Imbard, 1996]
and attains the ratio of anisotropy nearly one everywhere. 
Minimum resolution in high latitudes is about 65 km in the Arctic and 50 km in the Antarctic 
[Timmermann et al, 2005].

%% Other configurations with a higher resolution (1 deg, 0.5 deg, and 0.25 deg) have also 
%% been developed [DRAKKAR group, 2007].
%% The mean grid spacing is about 2/3 of the nominal value: for example it is 1.3 degrees for 
%% ORCA2. In the coarse resolution version such as ORCA2 the meridional grid spacing is 
%% increased near the equator to improve the equatorial dynamics.

In the vertical direction, the model uses a full or partial step z-coordinate or s-coordinate. 
There are 31 levels, with 10 levels in the top 100m and partial steps in the lowest level. 
The vertical mesh is deduced from a mathematical function of z [Madec and Imbard 1996]. 
Bottom topography and coastlines are derived from the ETOPO5 dataset and work of 
Smith and Sandwell (1997). The distribution of variables is a three-dimensional Arakawa C-type grid. 

In the ORCA2\_LIM\_PISCES configuration, lateral tracer mixing is done along isopycnals. 
Eddy induced tracer advection is parameterized following Gent and McWilliams (1990).
Horizontal momentum is mixed along model level surfaces using the eddy viscosity 
coefficients varying with latitude, longitude and depth.
Vertical eddy diffusivity and viscosity coefficients are calculated using a 1.5
order turbulent kinetic energy model [Gaspar et al., 1990].
%% Zero fluxes of heat and salt and no-slip conditions are applied through lateral solid 
%% boundaries. At the bottom boundary, zero fluxes of heat and salt are applied through the 
%% ocean bottom.

The ocean is subject to the external forcings of heat, freshwater, and momentum fluxes 
from the atmosphere and/or the sea-ice. The solar radiation penetrates the top meters of 
the ocean. The downward irradiance is formulated with two extinction coefficients 
[Paulson and Simpson, 1977], whose values correspond to a Type I water, the most 
transparent water, in Jerlov's classification [Jerlov, 1968].
We intend to adopt the parameterization proposed by Morel and Antoine [1994]
to improve the upper ocean solar heating rate affected by the abundance of phytoplankton
[Nakamoto, et al, 2001; Ueyoshi, et al, 2003; Ueyoshi, et al, 2005; Frouin, et al, 2007; 
Subrahmanyam, et al, 2007].

Solar radiation absorption and local heating within the upper layers of the ocean are
strongly influenced by the abundance of phytoplankton. Depending on the degree of the
chlorophyll concentration, the heat deposition occurs within a layer that may vary in 
thickness from less than 10 m to more than 100 m. Morel and Antoine's [1994]
parameterization allows the vertical profiles of heating rate to be predicted from 
the phytoplanktonic pigment concentration.
For the infrared waveband, not influenced by biological materials, the irradiance profile 
is described by a single exponential function. For the ultraviolet and visible %% ($<$ 750 nm)
band, a bimodal exponential form is adopted. The weights associated with each of these 
exponential functions, along with their specific attenuation lenghts, are dependent upon
pigment concentration. These dependencies are explicated through polynomial formulas.
Pigment values predicted by the PISCES model will be used for the heat rate calculation
(Morel and Antoine, 1994).
 
%% [Bougeault and Lacarrere, 1989, Gaspar et al., 1990; Blanke and Delecluse, 1993].
{\vskip 12pt}
{\noindent Sea-ice model:}
{\vskip 12pt}

Within NEMO, the ocean is interfaced with the interactive sea-ice model LIM3 
(Louvain-la-Neuve sea ice model) [Fichefet and Morales-Maqueda, 1997, 
Timmermann, et al, 2005]. LIM3 is a C-grid dynamic� thermodynamic model that includes the 
representation of the subgrid-scale distributions of five-category sea ice thickness, 
enthalpy, salinity and age. Brine entrapment and drainage as well as brine 
impact on ice thermodynamics are explicitly included (Vancoppenolle, et al, 2009).
%% LIM3 is found to significantly improve the simulation of sea ice characteristics 
%% compared to the earlier LIM versions making it a more appropriate and accurate tool not 
%% only in ice-ocean and climate simulations but also presumably for operational oceanography
%% (Vancoppenolle, et al, 2008).

%% http://www.climate.be/lim/index.php?id=49
%% LIM3 is the most recent version of LIM. It is a five-category sea ice thickness, enthalpy, salinity and 
%% age distribution model. The vertical ice growth and decay in each thickness category is determined by an 
%% energy conserving thermodynamic model with one layer of snow and five layers of ice. The effect of brine 
%% pockets on the ice thermal properties is explicitly accounted for. The surface albedo depends on the 
%% state of the surface, the snow and ice thicknesses, and the cloudiness. The model also includes a snow 
%% ice formation scheme. A linear remapping procedure is utilized to compute the transport in thickness 
%% space. For each thickness category, the bulk salinity of sea ice is calculated by taking into 
%% consideration brine entrapment during freezing and the most important brine drainage mechanisms, i.e., 
%% gravity drainage and flushing. The vertical sea ice salinity profile is parameterized as a function of 
%% this bulk salinity and the ice thickness. A parameterization of frazil ice production in open water areas 
%% is also incorporated. Ice dynamics are simulated by assuming that sea ice behaves as a two-dimensional 
%% elastic-viscous-plastic continuum in dynamical interaction with atmosphere and ocean. The ice momentum 
%% and transport equations are written in curvilinear, orthogonal coordinates and are numerically solved on 
%% a C-grid. For the transport equation, a numerical method that conserves the second-order moments of the 
%% spatial distribution of the advected quantity is used. Regarding the ice mechanical redistribution 
%% functions, they take into account both ridging and rafting processes as well as the influence of the 
%% ridge porosity. Finally, it is worth mentioning that the age of each ice thickness category is explicitly 
%% modeled. The code can be downloaded from the NEMO website .



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{\noindent Biogeochemical model:}
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The NEMO modeling framework includes PISCES based on the Hamburg Ocean Carbon Cycle 5
(HAMOCC5) model [Aumont et al., 2003; Aumont and Bopp 2006] 
(see http://www.meece.eu/documents/deliverables/WP2/D2.4.pdf).
%%  the Pelagic Interactions Scheme for Carbon
%%  and Ecosystem Studies (PISCES) ocean biogeochemistry model. 

PISCES is a biogeochemical model which simulates the marine biological productivity that 
describes the biogeochemical cycles of carbon and of the main nutrients (P, N, Si, Fe). 
%%  This model can be categorized as one of the many Monod models [Monod, 1942] since it 
%%  assumes a constant Redfield ratio and phytoplankton growth depends on external 
%%  concentration of nutrients.
PISCES assumes a constant Redfield ratio and phytoplankton growth is directly limited by
the external availability in nutrients [Monod, 1942] so that
%%  However, when modeling silicate, iron and/or chlorophyll, assuming constant ratios is not 
%%  justified anymore as these ratios can vary a lot (for instance, one order of magnitude for 
%%  the Fe/C ratio). Thus, 
the elemental ratios of Fe, Si and Chl are prognostically predicted 
based on external concentrations of the limiting nutrients. 
%%  like in the quota approach [McCarthy, 1980; Droop, 1983]. 
PISCES has currently 24 compartments. These are five modeled limiting nutrients for 
phytoplankton growth: Nitrate and Ammonium, Phosphate, Silicate and Iron. 
Phosphate and Nitrate+Ammonium are not really independent nutrients in 
PISCES since they are linked by constant Redfield ratios but the nitrogen pool 
undergoes nitrogen fixation and denitrification.

Four living compartments are represented: two phytoplankton size-classes/groups 
(nanophytplankton and diatoms) and two zooplankton size classes 
(microzooplankton and mesozooplankton). For phytoplankton, prognostic variables are total 
biomass, the iron, chlorophyll and silicon contents. This means that the Fe/C, Chl/C and 
Si/C ratios of both phytoplankton groups are fully predicted by the model. For 
zooplankton, only the total biomass is modeled. For all species, the O/C/N/P ratios are 
kept constant and are not allowed to vary.

%-----------------------------------------------------------------------
\subsection{
3.2 Simulations of Climate Change Impacts during the last Decade
}
{\vskip 12pt}
{\noindent
Atmospheric forcing fields:}
{\vskip 12pt}

The DFS4 dataset, a new set of 49-year-long (1958-2006) coarse-resolution (2 deg x 2 deg)
forcing variables for OGCMs based on ERA40 will be used as atmospheric forcing fields
at the ocean surface. The dataset has been extensively tested and proved that 
the refined ERA40 fields contributed to improve the representation of central 
features of the global ocean circulation [Brodeau, et al, 2010]. 
The dataset consists of 8 variables used for interannual forcing: 6-hourly wind velocity 
components at 10m, 6-hourly potential temperature and specific humidity at 2m, 
daily solar and infra-red downwelling radiation, and monthly total precipitation and snow.
The dataset is currently extended to year 2007 and is available from the Drakkar group
[The DRAKKAR Group, 2007; Brodeau, et al, 2006].

%% The hybrid forcing using CORE radiation fluxes and precipitation fields with
%% ERA40 turbulent variables (wind, air temperature and specific humidity), DFS3,
%% produces an Atlantic overturning circulation with the most realistic strength
%% in ~50-year hindcasts using higher resolution versions of ORCA models 
%% [The DRAKKAR Group, 2007]. 
We intend to use also the CORE.2 Global Air-Sea Flux dataset available 
from NCAR along with NCEP/NCAR daily reanalysis data [Large and Yeager, 2004;
(http://dss.ucar.edu/datasets/ds260.2/)].

%% %%  Nesting over the Arctic region:

%% %%  We intend to perform the experiments using a two-way nesting via the AGRIF software
%% %%  over the Arctic region [Debreu, et al, 2007].
%% %%  AGRIF is a package for the integration of adaptive mesh refinement (AMR) features within a 
%% %%  multidimensional model written in Fortran and discretized on a structured grid. 
%% %%  This nesting capability that allows resolution to be focused over a region of interest by 
%% %%  introducing an additional grid has been added to NEMO. In the current implementation only 
%% %%  horizontal refinement is available.
 
%% The way to run an embedded model by using the NEMO/
%% AGRIF framework in a pre-defined configuration is described at the website: http://
%% www.nemo-ocean.eu/Using-NEMO/].

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{\noindent
Biogeochemical data:}
{\vskip 12pt}

?? http://dodsp.idris.fr/reee224/
(See Aumont and Bopp, 2006). 

% -------------------------------------------------------------------------
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{\noindent Model experiments:}
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The simulation is initially conducted over the period 1958 to �2006 for which the DFS4.1 
ocean surface forcing datasets are available. The period will be extended
as the most recent DFS4 and other datasets such as NCEP/NCAR daily reanalysis data 
become available. 
%% We also intend to use the CORE.2 Global Air-Sea Flux dataset available 
%% from NCAR (http://dss.ucar.edu/datasets/ds260.2/)[Large and Yeager, 2004].

% Spinup
% http://valor.nerc.ac.uk/wiki/Model_spinup

Initial state at the time of the beginning of the simulations
is a January 1 state resulting from a spin-up run using climatological forcing fields.
In this spin-up run, the ocean is initially at rest with temperature and salinity set 
to January climatorogical values of Levitus (1982). 
From this initial state, the ORCA2\_LIM\_PISCES configuration of NEMO is 
integrated for 50 years with Newtonian restoring terms for sea surface salinity only.
For the ocean surface forcing, the CLIO bulk formula (Goosse, et al, 1999) is used 
with atmospheric monthly climatology data obtained from the 49-year NFS4.1 dataset.

%% One pass through the 1958-1967 or 1958-2006 forcing as a spinup for the simulation beginning 
%% at 01Jan1958 may be used. The spinup, however, needs to be examined and adjusted 
%% carefully depending on the simulations to perform (http://valor.nerc.ac.uk/wiki/Model_spinup).


%Sea-ice data:
Initial mean sea ice thicknesses of 3.5 m in the Arctic and 1 m in the Southern Ocean 
are imposed in regions with a sea surface temperature below 0 C. An initial snow cover 
with a thickness of 0.3 m in the Arctic and 0.1 m in the Antarctic is assumed.
Initial ice concentration is assumed to be 0.95 in the Arctic and 0.90 in the Antarctic
(Vancoppenolle, et al, 2009).
%% Initially, the ice thickness distribution is assumed to be 
%% Gaussian, age and velocity are prescribed to 0, salinity to 6‰ and ice and 
%% snow temperatures to 270 K (Vancoppenolle, et al, 2009).
% 1958-2006 sea-ice init
% >>> All simulations so far done used LIM2. <<<

{\vskip 12pt}
We plan to perform two experiments:
{\vskip 12pt}

{\noindent EXP 1:}
{\vskip 12pt}

We'll use the original ORCA2\_LIM\_PISCES configuration of the NEMO in which
the vertical profile of heating rate in the upper ocean is calculated using 
Paulson and Simpson's (1977) formula. It assumes a time- and space-invariant 
Type I water %%, the most transparent water,
in Jerlov's classification [Jerlov, 1968].

{\noindent EXP 2:} 
{\vskip 12pt}

We'll use Morel and Antonine's (1994) heating rate parameterization
that is dependent on chlorophyll concentrations and thus makes the heating rate
in the upper ocean both time- and space-variant.

{\vskip 12pt}
{\noindent Model output:}
{\vskip 12pt}

The output variables from ORCA2 are usual 3 velocity components, temperature, salinity, 
mixed-layer depth, etc.
The PIECES model output variables include, among others, concentrations of 
4 plankton functional types (nanophytoplankton, diatoms, meso and micro zooplankton)
on the 31 model levels at various time frequencies from daily to yearly. 
%% Also included are  pCO2, pO2, and alkalinity. 
The LIM3 variables include ice presence, ice thickness, ice surface temperature, 
and snow thickness.



Ice concentration in the Arctic from two experiments will be compared to each other and
the passive microwave observations (Comiso, 2007).
{\vskip 12pt}

Chlorophyll concentration in the Arctic will be compared to SeaWiFS data.
{\vskip 12pt}

We'll investigate whether simulated results show global long-term declining trends of 
chlorophyll concentration as in a observational study (Boyce, et al, 2010)
and if that is the case whether the trends are related to increasing sea surface temperature or 
mixed-layer depth anomalies.





\end{document}  
