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

Fast Predictive Image Registration

We present a method to predict image deformations based on patch-wise image appearance. Specifically, we design a patch-based deep encoder-decoder network which learns the pixel/voxel-wise mapping between image appearance and registration parameters. Our approach can predict general deformation parameterizations, however, we focus on the large deformation diffeomorphic metric mapping (LDDMM) registration model. By predicting the LDDMM momentum-parameterization we retain the desirable theoretical properties of LDDMM, while reducing computation time by orders of magnitude: combined with patch pruning, we achieve a 1500x/66x speed up compared to GPU-based optimization for 2D/3D image registration. Our approach has better prediction accuracy than predicting deformation or velocity fields and results in diffeomorphic transformations. Additionally, we create a Bayesian probabilistic version of our network, which allows evaluation of deformation field uncertainty through Monte Carlo sampling using dropout at test time. We show that deformation uncertainty highlights areas of ambiguous deformations. We test our method on the OASIS brain image dataset in 2D and 3D

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 $\textbf{B}_r$, 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 $\textbf{B}_r$ 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

Ocean- Atmosphere Interactions During Cyclone Nargis

Cyclone Nargis (Figure 1a) made landfall in Myanmar (formerly Burma) on 2 May 2008 with sustained winds of approximately 210 kilometers per hour, equivalent to a category 3– 4 hurricane. In addition, Nargis brought approximately 600 millimeters of rain and a storm surge of 3– 4 meters to the low- lying and densely populated Irrawaddy River delta. In its wake, the storm left an estimated 130,000 dead or missing and more than $10 billion in economic losses. It was the worst natural disaster to strike the Indian Ocean region since the 26 December 2004 tsunami and the worst recorded natural disaster ever to affect Myanmar

Salinity Measurements Collected by Fishermen Reveal a “River in the Sea” Flowing Along the Eastern Coast of India

Being the only tropical ocean bounded by a continent to the north, the Indian Ocean is home to the most powerful monsoon system on Earth. Monsoonal rains and winds induce huge river discharges and strong coastal currents in the northern Bay of Bengal. To date, the paucity of salinity data has prevented a thorough description of the spreading of this freshwater into the bay. The potential impact of the salinity on cyclones and regional climate in the Bay of Bengal is, however, a strong incentive for a better description of the water cycle in this region. Since May 2005, the National Institute of Oceanography conducts a program in which fishermen collect seawater samples in knee-deep water at eight stations along the Indian coastline every 5 days. Comparison with open-ocean samples shows that this cost-effective sampling strategy is representative of offshore salinity evolution. This new dataset reveals a salinity drop exceeding 10 g kg−1 in the northern part of the bay at the end of the summer monsoon. This freshening signal propagates southward in a narrow (~100 km wide) strip along the eastern coast of India, and reaches its southern tip after 2.5 months. Satellite-derived alongshore-current data shows that the southward propagation of this “river in the sea” is consistent with transport by seasonal coastal currents, while other processes are responsible for the ensuing erosion of this coastal freshening. This simple procedure of coastal seawater samples collection could further be used to monitor phytoplankton concentration, bacterial content, and isotopic composition of seawater along the Indian coastlin

The equatorial West Pacific fresh pool at the end of the La Nina event in October/November 1996

The salinity, temperature and current distributions have been measured during the TROPAC cruise (Oct./Nov. 1996) at two sections, i.e. 143°E and 150°E, during the final phase of the 1995/1996 La Niña. The results present evidence that the fresh pool and the salinity front at its eastern boundary had moved far to the west, and that a barrier layer existed in that phase. The observed currents support the idea that advective processes play an essential role in creating the thermohaline structure during this ENSO phase. In relation with this process, it is found that the westward subduction mechanism of relatively dense eastern equatorial waters may apply during that phase

CIRENE Air-Sea Interactions in the Seychelles-Chagos Thermocline Ridge Region

A field experiment in the southwestern Indian Ocean provides new insights into ocean-atmosphere interactions in a key climatic region

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

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):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 ocean–atmosphere 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 Niño–Southern 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 African–Asian–Australian 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

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