9,281 research outputs found
A 4D-Var Method with Flow-Dependent Background Covariances for the Shallow-Water Equations
The 4D-Var method for filtering partially observed nonlinear chaotic
dynamical systems consists of finding the maximum a-posteriori (MAP) estimator
of the initial condition of the system given observations over a time window,
and propagating it forward to the current time via the model dynamics. This
method forms the basis of most currently operational weather forecasting
systems. In practice the optimization becomes infeasible if the time window is
too long due to the non-convexity of the cost function, the effect of model
errors, and the limited precision of the ODE solvers. Hence the window has to
be kept sufficiently short, and the observations in the previous windows can be
taken into account via a Gaussian background (prior) distribution. The choice
of the background covariance matrix is an important question that has received
much attention in the literature. In this paper, we define the background
covariances in a principled manner, based on observations in the previous
assimilation windows, for a parameter . The method is at most times
more computationally expensive than using fixed background covariances,
requires little tuning, and greatly improves the accuracy of 4D-Var. As a
concrete example, we focus on the shallow-water equations. The proposed method
is compared against state-of-the-art approaches in data assimilation and is
shown to perform favourably on simulated data. We also illustrate our approach
on data from the recent tsunami of 2011 in Fukushima, Japan.Comment: 32 pages, 5 figure
Locating and quantifying gas emission sources using remotely obtained concentration data
We describe a method for detecting, locating and quantifying sources of gas
emissions to the atmosphere using remotely obtained gas concentration data; the
method is applicable to gases of environmental concern. We demonstrate its
performance using methane data collected from aircraft. Atmospheric point
concentration measurements are modelled as the sum of a spatially and
temporally smooth atmospheric background concentration, augmented by
concentrations due to local sources. We model source emission rates with a
Gaussian mixture model and use a Markov random field to represent the
atmospheric background concentration component of the measurements. A Gaussian
plume atmospheric eddy dispersion model represents gas dispersion between
sources and measurement locations. Initial point estimates of background
concentrations and source emission rates are obtained using mixed L2-L1
optimisation over a discretised grid of potential source locations. Subsequent
reversible jump Markov chain Monte Carlo inference provides estimated values
and uncertainties for the number, emission rates and locations of sources
unconstrained by a grid. Source area, atmospheric background concentrations and
other model parameters are also estimated. We investigate the performance of
the approach first using a synthetic problem, then apply the method to real
data collected from an aircraft flying over: a 1600 km^2 area containing two
landfills, then a 225 km^2 area containing a gas flare stack
Efficient and Stable Acoustic Tomography Using Sparse Reconstruction Methods
We study an acoustic tomography problem and propose a new inversion technique based on sparsity. Acoustic tomography observes the parameters of the medium that influence the speed of sound propagation. In the human body, the parameters that mostly influence the sound speed are temperature and density, in the ocean - temperature and current, in the atmosphere - temperature and wind. In this study, we focus on estimating temperature in the atmosphere using the information on the average sound speed along the propagation path. The latter is practically obtained from travel time measurements. We propose a reconstruction algorithm that exploits the concept of sparsity. Namely, the temperature is assumed to be a linear combination of some functions (e.g. bases or set of different bases) where many of the coefficients are known to be zero. The goal is to find the non-zero coefficients. To this end, we apply an algorithm based on linear programming that under some constrains finds the solution with minimum l0 norm. This is actually equivalent to the fact that many of the unknown coefficients are zeros. Finally, we perform numerical simulations to assess the effectiveness of our approach. The simulation results confirm the applicability of the method and demonstrate high reconstruction quality and robustness to noise
ADAM: a general method for using various data types in asteroid reconstruction
We introduce ADAM, the All-Data Asteroid Modelling algorithm. ADAM is simple
and universal since it handles all disk-resolved data types (adaptive optics or
other images, interferometry, and range-Doppler radar data) in a uniform manner
via the 2D Fourier transform, enabling fast convergence in model optimization.
The resolved data can be combined with disk-integrated data (photometry). In
the reconstruction process, the difference between each data type is only a few
code lines defining the particular generalized projection from 3D onto a 2D
image plane. Occultation timings can be included as sparse silhouettes, and
thermal infrared data are efficiently handled with an approximate algorithm
that is sufficient in practice due to the dominance of the high-contrast
(boundary) pixels over the low-contrast (interior) ones. This is of particular
importance to the raw ALMA data that can be directly handled by ADAM without
having to construct the standard image. We study the reliability of the
inversion by using the independent shape supports of function series and
control-point surfaces. When other data are lacking, one can carry out fast
nonconvex lightcurve-only inversion, but any shape models resulting from it
should only be taken as illustrative global-scale ones.Comment: 11 pages, submitted to A&
Variational Data Assimilation via Sparse Regularization
This paper studies the role of sparse regularization in a properly chosen
basis for variational data assimilation (VDA) problems. Specifically, it
focuses on data assimilation of noisy and down-sampled observations while the
state variable of interest exhibits sparsity in the real or transformed domain.
We show that in the presence of sparsity, the -norm regularization
produces more accurate and stable solutions than the classic data assimilation
methods. To motivate further developments of the proposed methodology,
assimilation experiments are conducted in the wavelet and spectral domain using
the linear advection-diffusion equation
Parallelizable sparse inverse formulation Gaussian processes (SpInGP)
We propose a parallelizable sparse inverse formulation Gaussian process
(SpInGP) for temporal models. It uses a sparse precision GP formulation and
sparse matrix routines to speed up the computations. Due to the state-space
formulation used in the algorithm, the time complexity of the basic SpInGP is
linear, and because all the computations are parallelizable, the parallel form
of the algorithm is sublinear in the number of data points. We provide example
algorithms to implement the sparse matrix routines and experimentally test the
method using both simulated and real data.Comment: Presented at Machine Learning in Signal Processing (MLSP2017
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