 In
our fluid laboratory we study geophysical fluid phenomena by physically
simulating flows, observing them using sensors and assimilating
observations with dynamical models. The laboratory approach
provides a basis for controlled experimentation of real
phenomena and serves a number of purposes, including:
- Classroom
education
- development of techniques: for motion estimation
from visual observations, state-estimation and predictability,
targeted/adaptive observations, distributed computation,
visualization, information retrieval
- the design of better
numerical models.
Here, we discuss the components of this
research program and several applications where this laboratory
has proved instrumental.
The GFD lab
The GFD laboratory
consists of several
turntables with cameras providing a birds-eye view in the
rotating frame of reference. The camera is connected to a local
sub-cluster which processes observations in a distributed manner
and delivers them to a cluster backbone for interfacing with
assimilation routines. Observations of fluorescent dye and
particles under motion are made at particular surfaces using
lasers to illuminate the surfaces of interest. In addition
observations of temperature are also made.
The cluster backbone
implements both the assimilation methods and numerical models. The
architecture of the cluster comprises of a large array of Intel
platforms connected with a extremely high-speed interconnect, and
distributed implementations of the the model and assimilation
performed using an MPI layer to handle communication.
One of the
most significant driving philosophies of our system is to keep it
simple! Common off the shelf components readily dominate all
aspects of this approach.
Processing observations
Three classes of
algorithms are used to estimate visual motion:
- particle tracking, where individual particles are tracked over
multiple imaged frames and the problems of interest are
predominated by tracking the correspondence between frame; we
employ probabilistic models to track particles.
- optic flow where patterns of
particles are tracked. In this class, robust, hierarchical least
squares techniques are employed to recover flow.
- tracking the evolution of interfaces and
volumes of dye in the fluid and represents some of the toughest
challenges to motion estimation.
Assimilation
Two pivotal technologies
are employed for data-assimilation or state estimation. The first
is statistical and uses the Ensemble Kalman Filter and variants.
The second is a constrained optimization approach based on the
adjoint of a numerical forward model. The constrained optimization
technique is geared to recover unknown or uncertain initial states
of the model, while the ensemble based methods are designed to
evolve initial distributions towards to the true system attractor
and are, in fact, implemented using Monte Carlo methods. Both
methods place an enormous computational burden and require careful
attention to distributed implementations.
Numerical modeling
Several numerical models
are used to describe the dynamics of the process under study. In
the classroom, such models are derived from appropriate governing
equations and their approximations, whereas in our research we
uniformly employ the MITgcm.
Read here about the
simulation
of a laboratory experiment using MITgcm.
The Hadley Experiment
A simple Hadley experiment serves as a starting point for
many of our research questions. A slowly rotating tank is
subject to thermal forcing in the form of a cold center (ice
bucket!) and a warm exterior. This sets up a Hadley like
circulation with the cold water in the center sinking to the
bottom and being replaced by warm water at the periphery. The
system maintains thermal-wind balance and geostrophy at the
surface. For a more detailed classroom experiment
see here.
The Hadley experiment was simulated
numerically using MITgcm and surface observations extracted using
the optic flow computed from moving pepper
particles! The assimilation method used the Ensemble Square Root
Filter, an approximation of the full Ensemble Kalman filter that
serially processes spatial observations under the assumptions of
diagonal observational covariances and correlation length-scale
between elements of state and the location of observation.
While
this experiment is somewhat simple from a state-estimation point
of view, it does require us to bring up the entire system
and consider issues that are encountered in the operational NWP
community.
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