**Predictive Understanding of the Oceans:**

**Wind-Driven Circulation on Interdecadal Time Scales**

## Michael Ghil, P.I., Dept. of Atmos. Sciences & IGPP, UCLA

## Roger Temam, Co-P.I., Dept. of Mathematics, Indiana University

## Y. Feliks, IIBR, E. Simonnet, INLN, & T. Tachim-Medjo, FIU, collaborators

#### Summary

***The goal of the proposed work is to obtain a predictive understanding
of a major component of the climate system's interdecadal variability:
the*** ***oceans' wind-driven circulation. To do so, we develop and
apply advanced computational and statistical methods to the problem of
climate variability and climate change. The methodology is being
developed first for models of intermediate complexity, such as the
quasi-geostrophic and the primitive equations, which describe the
wind-driven, near-surface flow in mid-latitude ocean basins. Our
computational work consists in developing efficient multi-level methods
to simulate this flow and study its dependence on physically relevant
parameters. Our oceanographic and climate work consists in applying
these methods to study the bifurcations in the wind-driven circulation
and their relevance to the flows observed at present and those that
might occur in a warmer climate. Both aspects of the work are crucial
for the efficient treatment of large-scale, eddy-resolving numerical
simulations of the oceans and an increased understanding of climate
change.***

**1. Introduction and motivation**

A large subtropical, anticyclonic gyre and a smaller, subpolar, cyclonic
gyre dominate the large-scale flow of the mid-latitude ocean basins.
These two gyres are driven by the shear in the winds that cross these
basins. They share the eastward extension of western boundary currents,
such as the Gulf Stream or Kuroshio. The boundary currents and eastward
jets carry large amounts of mass, heat, momentum and trace substances.
They substantially affect the surface temperatures and precipitation
pattern over the adjacent land masses.

To understand the oceanic circulation's interdecadal variability, it is
essential to (i) carry out long integrations of high-resolution,
realistic ocean models; and (ii) obtain a complete picture of how the
oceanic flows' behavior changes as various climatic parameters change.
So far the low-frequency variability of the double-gyre circulation has
been studied mostly in simple-to-intermediate models by using the
analytical and numerical methods of dynamical systems theory. The
competing instabilities present in these models give rise to variability
with time scales of a few months to a few decades. We aim to understand
and predict this variability, using the novel computational resources
provided by terascale devices.

To achieve this goal, we study a hierarchy of ocean models, from
quasi-geostrophic (QG through shallow-water (SW) and on to
primitive-equation (PE) models. The latter are very close to the most
realistic general circulation models (GCMs) used today in studying ocean
variability. At each level of the hierarchy, we consider increasing
horizontal and vertical resolution.

**2. Main results**

From the dynamical point of view, major progress has been made this year
in understanding the low-frequency variability (LFV) of the wind-driven
double-gyre circulation. Nonlinear instabilities that produce
interannual relaxation oscillations of the eastward jets arise through
global, homoclinic bifurcations as the wind stress increases or
dissipation decreases **\[6\]**.

We have initiated the study of coupled, high-resolution
ocean--atmosphere models in a mid-latitude basin that account for the
thermal effects of oceanic fronts on the atmospheric jet above.
Preliminary results indicate that interannual variability of the storm
track may be produced in this way **\[2\]**. These results, first
obtained with a very simple QG atmospheric model, seem to persist for
more realistic models as well.

From the computational point of view, we have been able to provide
several new numerical approaches for the study of the long-term dynamics
of PE models. Based on the small depth-to-length aspect ratio of the
oceans, we demonstrated the smallness of the baroclinic component of
mid-latitude oceanic flows and used this smallness to derive new
algorithms for capturing the low-frequency dynamics correctly **\[5\]**.

We expect, furthermore, to derive algorithms that approximate the
low-frequency dynamics of the double-gyre circulation by slaving the
higher-frequency dynamics to it in a statistical way. We are also
developing new numerical algorithms that solve an asymptotic version of
the PEs, expanded with respect to the vertical aspect ratio **\[4\]**.

**Collaborations**. This research is being carried out in close
collaboration between the climate dynamics group at UCLA (headed by the
P.I., Michael Ghil) and the numerical mathematics group at Indiana
University (headed by the Co-P.I., Roger Temam). Additional institutions
involved in the project are Colorado State University (Prof. Henk A.
Dijkstra), Florida International University (Prof. Theodore
Tachim-Medjo), Institut Non-Lineaire de Nice, France (Dr. Eric
Simonnet), and Israel Institute for Biological Research, Israel (Dr.
Yizhak Feliks). The SciDAC project provides us with a unique opportunity
to exploit the power of terascale computing as well as to bring together
a strong group of investigators with complementary knowledge, interests
and skills.

Our work represents an important step in advancing multi-level and
numerical bifurcation methods for partial differential equations in
continuum mechanics. In this broader perspective, we have discussed our
work or collaborated with Len Margolin (LANL) and Joseph J. Tribbia
(NCAR) (e.g., at the Summer School on Mathematics and Computations in
the Atmospheric and Oceanic Sciences, Boulder, Colo., 2003; see also
**\[1\]**).

**Most recent products delivered:**

**\[1\]** Dubois**,** T., F. Jauberteau, R. Temam, & J. Tribbia, 2004:
Different time schemes to compute the large and small scales for the
shallow-water problem, *J. Comp. Phys*., submitted.

**\[2\]** Feliks, Y., M. Ghil, & E. Simonnet, 2004: Low-frequency
variability in the mid-latitude atmosphere induced by an oceanic thermal
front, *J. Atmos. Sci*., in press.

**\[3\]** Simonnet, E., T. Tachim-Medjo, & R.Temam, 2003a:
Barotropic-baroclinic formulation of the primitive equations of the
ocean, *Appl. Analysis*, 82:439\--456.

**\[4\]** Simonnet, E., T. Tachim-Medjo, & R.Temam, 2003b: Higher-order
approximation equations for the primitive equations of the ocean, Proc.
Erice Conf., to appear.

**\[5\]** Simonnet, E., T. Tachim-Medjo, & R.Temam, 2004a: On the order
of magnitude of the baroclinic flow in the primitive equations of the
oceans, Annali Matematica Pura Appl., submitted.

**\[6\]** Simonnet, E., M.Ghil, & H.A. Dijkstra, 2004: Homoclinic
bifurcations in the barotropic quasi-geostrophic double-gyre
circulation, *J. Phys. Oceanogr*., *sub judice*.