Ariane, a Lagrangian analysis application for ocean circulation models
developed by Bruno Blanke and Nicolas Grima
Qualitative approach
In this sixth part,
we will present the idea behind some of the diagnostics
that can be performed from the calculation of these Lagrangian trajectories.
In the Ariane formalism,
we usually distinguish between qualitative
and quantitative approaches.
In a qualitative approach,
we are interested in the details of individual trajectories.
This allows us to illustrate general features of ocean circulation
as modelled by the calculation code that produced the velocity fields.
A trajectory is defined by a temporal succession of geographical positions:
longitude, latitude and depth,
on which the physical properties of the ocean,
temperature and salinity, or the geochemical properties,
if the ocean model has been integrated with a tracer code, are known.
There are multiple possible projection planes to show the trajectories,
possibly using colour to represent a third dimension.
The simplest representation
is the visualisation of the movement on the horizontal,
with colour to indicate the depth.
But one can also project the trajectories
in a salinity-temperature diagram,
for example to highlight water mass conversions.
An example of a qualitative approach
is the illustration of the thermohaline circulation
on the home page of Ariane.
The ocean model that was used to produce the velocity field
is the OPA model,
the ocean component of the NEMO code
in a low-resolution global version.
The model grid is a C-grid.
The grid mesh beyond 20°N is no longer aligned
along latitudes and longitudes
to avoid the numerical singularity of the North Pole.
The resolution of the model is 2° in longitude
and from 0.5°, at the equator,
to 1.5° in latitude.
There are 31 vertical levels
with a resolution of 10 m in the surface layers
and 500 m in the deeper layers.
The simulation is climatological.
The forcing functions applied to the ocean model
are monthly or seasonal climatologies
for wind stress,
heat fluxes
and surface salinity.
In its equations for temperature and salinity,
the model also includes a restoring term to climatologies.
This restoring is applied everywhere,
except near the coast,
equator and surface,
where the model dynamics are able to reproduce finer structures
than those resolved in these climatologies.
In this configuration,
the model essentially acts as a dynamic interpolator
of a density field known by its temperature and salinity climatology.
The model computes a three-dimensional circulation,
consistent with the surface forcing
and the time-variable ocean density field.
Because the resolution of the model is coarse,
this circulation
does not include fine-scale eddies
or intra-month variability.
After a few decades of integration,
the model simulation stabilises
on an annual cycle that tends to repeat itself identically.
In order to archive the model, is therefore legitimate to keep
only the last year of integration.
We thus have a monthly archive of 12 months of velocity components:
U, V and W,
and tracers:
T, S and density.
The Lagrangian diagnostics
will be built on this archive,
with the possibility of looping on it
to calculate trajectories longer than one year.
In other words,
the months of December and January can be linked
in the same way as January and February,
in the context chosen for the climatological simulation.
Even if it is only a qualitative illustration,
the pedagogic and scientific interest
of visualising an individual trajectory is obvious.
With an initial position chosen in the surface layers of the Indonesian Throughflow,
we highlight the journey of a numerical particle
through all the oceans of the globe.
The Indian Ocean first,
then the Atlantic Ocean from south to north
is traversed mostly at the surface.
The severe meteorological conditions in the Arctic Ocean,
with icy winds and very strong evaporation,
lead the surface water to densify
and sink to great depths.
This is the path taken by the particle
before returning to the southern hemisphere,
by crossing the entire Atlantic
in a deep vein along the American continent.
After several revolutions around Antarctica,
in the Antarctic Circumpolar Current,
the particle gradually rises in the water column.
It then reaches the Pacific Ocean,
where it recirculates in the equatorial region,
before entering the Indian Ocean by the Indonesian Throughflow.
The geography of the successive positions,
their depths, but also the transit times,
are all qualitative information
useful for understanding global ocean circulation.
As an indication,
the whole of the journey I just related
takes about 500 years for the particle,
but only a few fractions of a second of CPU time.
This Lagrangian trajectory
served as the basis for a documentary co-produced by Arte and Radio Canada.
It was indeed the main thread of the film 'Voyage au centre de la mer'.
Different oceanic processes,
or coupled processes between the ocean and the atmosphere,
important for the climate or marine ecosystems,
were discussed at key stages of this global trajectory.
We can multiply the initial positions
and generate a larger number of trajectories
whose behaviours will, of course, differ and can be compared.
Small differences in the initial geographical position
or in the departure date in the year
quickly lead to large differences in the destinations reached
or in the evolution of physical and geochemical properties along the trajectories.
It is possible to perform statistics
based on this qualitative approach,
working on a large number of individual trajectories.
For example, dispersion studies are possible.
But one quickly runs into at least two problems.
First, storing the successive positions of thousands (even millions) of particles
can become very cumbersome to handle.
Second, the diagnostics can be biased or incomplete,
because of the arbitrary choice of particles and their initial positions.
This is the reason why Ariane integrates in its calculations
a module that allows a quantitative approach to Lagrangian diagnostics.
Here, I've put a paragraph from a scientific article published a few years ago,
which presented the tools and rationale
of Lagrangian diagnostics applied to the ocean.
The Ariane tool is a pioneering tool
for the development of reliable quantitative analyses,
based on the Lagrangian trajectories,
which we have just introduced.
One of the innovative approaches we have proposed
is the notion of Lagrangian stream function,
which allows the quantification and visualisation
of water exchanges between two distant regions of the ocean.