230 research outputs found
Bayesian data assimilation in shape registration
In this paper we apply a Bayesian framework to the problem of geodesic curve matching. Given a template curve, the geodesic equations provide a mapping from initial conditions\ud
for the conjugate momentum onto topologically equivalent shapes. Here, we aim to recover the well defined posterior distribution on the initial momentum which gives rise to observed points on the target curve; this is achieved by explicitly including a reparameterisation in the formulation. Appropriate priors are chosen for the functions which together determine this field and the positions of the observation points, the initial momentum p0 and the reparameterisation vector field v, informed by regularity results about the forward model. Having done this, we illustrate how Maximum Likelihood Estimators (MLEs) can be used to find regions of high posterior density, but also how we can apply recently developed MCMC methods on function spaces to characterise the whole of the posterior density. These illustrative examples also include scenarios where the posterior distribution is multimodal and irregular, leading us to the conclusion that knowledge of a state of global maximal posterior density does not always give us the whole picture, and full posterior sampling can give better quantification of likely states and the overall uncertainty inherent in the problem
Mixture of Kernels and Iterated Semidirect Product of Diffeomorphisms Groups
In the framework of large deformation diffeomorphic metric mapping (LDDMM),
we develop a multi-scale theory for the diffeomorphism group based on previous
works. The purpose of the paper is (1) to develop in details a variational
approach for multi-scale analysis of diffeomorphisms, (2) to generalise to
several scales the semidirect product representation and (3) to illustrate the
resulting diffeomorphic decomposition on synthetic and real images. We also
show that the approaches presented in other papers and the mixture of kernels
are equivalent.Comment: 21 pages, revised version without section on evaluatio
A reduced-order strategy for 4D-Var data assimilation
This paper presents a reduced-order approach for four-dimensional variational
data assimilation, based on a prior EO F analysis of a model trajectory. This
method implies two main advantages: a natural model-based definition of a mul
tivariate background error covariance matrix , and an important
decrease of the computational burden o f the method, due to the drastic
reduction of the dimension of the control space. % An illustration of the
feasibility and the effectiveness of this method is given in the academic
framework of twin experiments for a model of the equatorial Pacific ocean. It
is shown that the multivariate aspect of brings additional
information which substantially improves the identification procedure. Moreover
the computational cost can be decreased by one order of magnitude with regard
to the full-space 4D-Var method
RAMA : the Research Moored Array for AfricanâAsianâAustralian Monsoon Analysis and Prediction
Author Posting. © American Meteorological Society, 2009. This article is posted here by permission of American Meteorological Society for personal use, not for redistribution. The definitive version was published in Bulletin of the American Meteorological Society 90 (2009):459-480, doi:10.1175/2008BAMS2608.1.The Indian Ocean is unique among the three tropical ocean basins in that it is blocked at 25°N by the Asian landmass. Seasonal heating and cooling of the land sets the stage for dramatic monsoon wind reversals, strong oceanâatmosphere interactions, and intense seasonal rains over the Indian subcontinent, Southeast Asia, East Africa, and Australia. Recurrence of these monsoon rains is critical to agricultural production that supports a third of the world's population. The Indian Ocean also remotely influences the evolution of El NiñoâSouthern Oscillation (ENSO), the North Atlantic Oscillation (NAO), North American weather, and hurricane activity. Despite its importance in the regional and global climate system though, the Indian Ocean is the most poorly observed and least well understood of the three tropical oceans.
This article describes the Research Moored Array for AfricanâAsianâAustralian Monsoon Analysis and Prediction (RAMA), a new observational network designed to address outstanding scientific questions related to Indian Ocean variability and the monsoons. RAMA is a multinationally supported element of the Indian Ocean Observing System (IndOOS), a combination of complementary satellite and in situ measurement platforms for climate research and forecasting. The article discusses the scientific rationale, design criteria, and implementation of the array. Initial RAMA data are presented to illustrate how they contribute to improved documentation and understanding of phenomena in the region. Applications of the data for societal benefit are also described
Un-reduction
This paper provides a full geometric development of a new technique called
un-reduction, for dealing with dynamics and optimal control problems posed on
spaces that are unwieldy for numerical implementation. The technique, which was
originally concieved for an application to image dynamics, uses Lagrangian
reduction by symmetry in reverse. A deeper understanding of un-reduction leads
to new developments in image matching which serve to illustrate the
mathematical power of the technique.Comment: 25 pages, revised versio
Supplement to RAMA : the Research Moored Array for African-Asian-Australian Monsoon Analysis and Prediction
Author Posting. © American Meteorological Society, 2009. This article is posted here by permission of American Meteorological Society for personal use, not for redistribution. The definitive version was published in Bulletin of the American Meteorological Society 90 (2009): ES5-ES8, doi:10.1175/2008BAMS2608.2
Invariant higher-order variational problems II
Motivated by applications in computational anatomy, we consider a
second-order problem in the calculus of variations on object manifolds that are
acted upon by Lie groups of smooth invertible transformations. This problem
leads to solution curves known as Riemannian cubics on object manifolds that
are endowed with normal metrics. The prime examples of such object manifolds
are the symmetric spaces. We characterize the class of cubics on object
manifolds that can be lifted horizontally to cubics on the group of
transformations. Conversely, we show that certain types of non-horizontal
geodesics on the group of transformations project to cubics. Finally, we apply
second-order Lagrange--Poincar\'e reduction to the problem of Riemannian cubics
on the group of transformations. This leads to a reduced form of the equations
that reveals the obstruction for the projection of a cubic on a transformation
group to again be a cubic on its object manifold.Comment: 40 pages, 1 figure. First version -- comments welcome
Cirene : air-sea iInteractions in the Seychelles-Chagos thermocline ridge region
Author Posting. © American Meteorological Society, 2009. This article is posted here by permission of American Meteorological Society for personal use, not for redistribution. The definitive version was published in Bulletin of the American Meteorological Society 90 (2009): 1337-1350, doi:10.1175/2008BAMS2499.1.The VascoâCirene program ex-plores how strong airâsea inter-actions promoted by the shallow thermocline and high sea surface temperature in the SeychellesâChagos thermocline ridge results in marked variability at synoptic, intraseasonal, and interannual time scales. The Cirene oceano-graphic cruise collected oceanic, atmospheric, and airâsea flux observations in this region in Jan-uaryâFebruary 2007. The contem-poraneous Vasco field experiment complemented these measure-ments with balloon deployments from the Seychelles. Cirene also contributed to the development of the Indian Ocean observing system via deployment of a moor-ing and 12 Argo profilers.
Unusual conditions prevailed in the Indian Ocean during Janu-ary and February 2007, following the Indian Ocean dipole climate anomaly of late 2006. Cirene measurements show that the SeychellesâChagos thermocline ridge had higher-than-usual heat content with subsurface anomalies up to 7°C. The ocean surface was warmer and fresher than average, and unusual eastward currents prevailed down to 800 m. These anomalous conditions had a major impact on tuna fishing in early 2007. Our dataset also sampled the genesis and maturation of Tropical Cyclone Dora, including high surface temperatures and a strong diurnal cycle before the cyclone, followed by a 1.5°C cool-ing over 10 days. Balloonborne instruments sampled the surface and boundary layer dynamics of Dora. We observed small-scale structures like dry-air layers in the atmosphere and diurnal warm layers in the near-surface ocean. The Cirene data will quantify the impact of these finescale features on the upper-ocean heat budget and atmospheric deep convection.CNES funded the Vasco part of the experiment; INSU
funded the Cirene part. R/V SuroĂźt is an Ifremer ship. The
contributions from ODU, WHOI, and FOI (Sweden) are
supported by the National Science Foundation under Grant
Number 0525657. The participation of the University of
Miami group was funded though NASA (NNG04HZ33C).
PMEL participation was supported through NOAAâs Office
of Climate Observation
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