 |
| Titel |
Gradient descent assimilation for the point-vortex model |
| VerfasserIn |
E. B. Suckling, L. A. Smith |
| Konferenz |
EGU General Assembly 2012
|
| Medientyp |
Artikel
|
| Sprache |
Englisch
|
| Digitales Dokument |
PDF |
| Erschienen |
In: GRA - Volume 14 (2012) |
| Datensatznummer |
250067341
|
|
|
|
|
|
| Zusammenfassung |
| Data assimilation is concerned with incorporating (noisy) observations into (imperfect)
models that describe the underlying dynamics of the system, in order to infer the properties of
the current state, by ensuring that the assimilated trajectories are consistent with both the
observations and model dynamics. For many physical systems, particularly in oceanography,
observations are usually available in the form of Lagrangian (particle trajectory) data
that are augmented into models describing the flow fields. The incorporation of
Lagrangian data into models of flow presents several challenges concerning the
potential complexity of the Lagrangian trajectories in relatively simple flow fields, for
example the appearance of nonlinear effects that are triggered by the exponential
rate of separation of tracer trajectories in the region of saddle points [1]. As such,
standard linear-based data assimilation methods, such as the Kalman filter, can
fail.
A nonlinear approach known as gradient descent assimilation [2] is presented, in which
analysis trajectories are found by minimising a cost function in an extended state
space. The gradient descent approach is demonstrated in the context of assimilating
Lagrangian tracer trajectories in two-dimensional flows of point-vortex systems. The
point-vortex model plays an important role as a simplified version of many physical
systems, including Bose-Einstein condensates, certain plasma configurations and
inviscid turbulence, in which the model dynamics are described by a relatively
simple system of nonlinear ODEs, which can exhibit regular or chaotic motion for
the 2-point vortex or 3-point vortex system respectively. A set of tracer advection
equations augment the point vortex model equations, allowing the observed tracer
positions to update the state information about the unobserved vortex postions. The
gradient descent approach to the two-point vortex system has been successfully
demonstrated for the case of both full and partial observations in a wide variety of test
cases.
[1] K. Ide, L. Kuznetsov and C. K. R. T. Jones. Lagrangian data assimilation for point vortex
systems, Journal of Turbulence, 3, 053 (2002).
[2] K. Judd, L. A. Smith and A. Weisheimer. Gradient free descent: Shadowing and state
estimation using limited derivative information, Physica D, 190, 153-166 (2004). |
|
|
|
|
|
|