218 research outputs found
Modeling extreme values of processes observed at irregular time steps: Application to significant wave height
This work is motivated by the analysis of the extremal behavior of buoy and
satellite data describing wave conditions in the North Atlantic Ocean. The
available data sets consist of time series of significant wave height (Hs) with
irregular time sampling. In such a situation, the usual statistical methods for
analyzing extreme values cannot be used directly. The method proposed in this
paper is an extension of the peaks over threshold (POT) method, where the
distribution of a process above a high threshold is approximated by a
max-stable process whose parameters are estimated by maximizing a composite
likelihood function. The efficiency of the proposed method is assessed on an
extensive set of simulated data. It is shown, in particular, that the method is
able to describe the extremal behavior of several common time series models
with regular or irregular time sampling. The method is then used to analyze Hs
data in the North Atlantic Ocean. The results indicate that it is possible to
derive realistic estimates of the extremal properties of Hs from satellite
data, despite its complex space--time sampling.Comment: Published in at http://dx.doi.org/10.1214/13-AOAS711 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Bayesian approach to Spatio-temporally Consistent Simulation of Daily Monsoon Rainfall over India
Simulation of rainfall over a region for long time-sequences can be very
useful for planning and policy-making, especially in India where the economy is
heavily reliant on monsoon rainfall. However, such simulations should be able
to preserve the known spatial and temporal characteristics of rainfall over
India. General Circulation Models (GCMs) are unable to do so, and various
rainfall generators designed by hydrologists using stochastic processes like
Gaussian Processes are also difficult to apply over the vast and highly diverse
landscape of India. In this paper, we explore a series of Bayesian models based
on conditional distributions of latent variables that describe weather
conditions at specific locations and over the whole country. During parameter
estimation from observed data, we use spatio-temporal smoothing using Markov
Random Field so that the parameters learnt are spatially and temporally
coherent. Also, we use a nonparametric spatial clustering based on Chinese
Restaurant Process to identify homogeneous regions, which are utilized by some
of the proposed models to improve spatial correlations of the simulated
rainfall. The models are able to simulate daily rainfall across India for
years, and can also utilize contextual information for conditional simulation.
We use two datasets of different spatial resolutions over India, and focus on
the period 2000-2015. We propose a large number of metrics to study the
spatio-temporal properties of the simulations by the models, and compare them
with the observed data to evaluate the strengths and weaknesses of the models
Sparse vector Markov switching autoregressive models. Application to multivariate time series of temperature
International audienceMultivariate time series are of interest in many fields including economics and environment. The dynamical processes occurring in these domains often exhibit regimes so that it is common to describe them using Markov Switching vector autoregressive processes. However the estimation of such models is difficult even when the dimension is not so high because of the number of parameters involved. In this paper we propose to use a Smoothly Clipped Absolute DEviation (SCAD) penalization of the likelihood to shrink the parameters. The Expectation Maximization algorithm build for maximizing the penalized likelihood is described in details and tested on daily mean temperature time series
The analog data assimilation
In light of growing interest in data-driven methods for oceanic, atmospheric, and climate sciences, this work focuses on the field of data assimilation and presents the analog data assimilation (AnDA). The proposed framework produces a reconstruction of the system dynamics in a fully data-driven manner where no explicit knowledge of the dynamical model is required. Instead, a representative catalog of trajectories of the system is assumed to be available. Based on this catalog, the analog data assimilation combines the nonparametric sampling of the dynamics using analog forecasting methods with ensemble-based assimilation techniques. This study explores different analog forecasting strategies and derives both ensemble Kalman and particle filtering versions of the proposed analog data assimilation approach. Numerical experiments are examined for two chaotic dynamical systems: the Lorenz-63 and Lorenz-96 systems. The performance of the analog data assimilation is discussed with respect to classical model-driven assimilation. A Matlab toolbox and Python library of the AnDA are provided to help further research building upon the present findings.Fil: Lguensat, Redouane. UniversitĂ© Bretagne Loire; FranciaFil: Tandeo, Pierre. UniversitĂ© Bretagne Loire; FranciaFil: Ailliot, Pierre. University of Western Brittany. Laboratoire de MathĂ©matiques de Bretagne Atlantique; FranciaFil: Pulido, Manuel Arturo. Consejo Nacional de Investigaciones CientĂficas y TĂ©cnicas. Centro CientĂfico TecnolĂłgico Conicet - Nordeste. Instituto de Modelado e InnovaciĂłn TecnolĂłgica. Universidad Nacional del Nordeste. Facultad de Ciencias Exactas Naturales y Agrimensura. Instituto de Modelado e InnovaciĂłn TecnolĂłgica; ArgentinaFil: Fablet, Ronan. UniversitĂ© Bretagne Loire; Franci
Markov-switching autoregressive models for wind time series
International audienceIn this paper, non-homogeneous Markov-Switching Autoregressive (MS-AR) models are proposed to describe wind time series. In these models, several au-toregressive models are used to describe the time evolution of the wind speed and the switching between these different models is controlled by a hidden Markov chain which represents the weather types. We first block the data by month in order to remove seasonal components and propose a MS-AR model with non-homogeneous autoregressive models to describe daily components. Then we discuss extensions where the hidden Markov chain is also non-stationary to handle seasonal and inter-annual fluctuations. The different models are fitted using the EM algorithm to a long time series of wind speed measurement on the Island of Ouessant (France). It is shown that the fitted models are interpretable and provide a good description of im-portant properties of the data such as the marginal distributions, the second-order structure or the length of the stormy and calm periods
Locally-adapted convolution-based super-resolution of irregularly-sampled ocean remote sensing data
Super-resolution is a classical problem in image processing, with numerous
applications to remote sensing image enhancement. Here, we address the
super-resolution of irregularly-sampled remote sensing images. Using an optimal
interpolation as the low-resolution reconstruction, we explore locally-adapted
multimodal convolutional models and investigate different dictionary-based
decompositions, namely based on principal component analysis (PCA), sparse
priors and non-negativity constraints. We consider an application to the
reconstruction of sea surface height (SSH) fields from two information sources,
along-track altimeter data and sea surface temperature (SST) data. The reported
experiments demonstrate the relevance of the proposed model, especially
locally-adapted parametrizations with non-negativity constraints, to outperform
optimally-interpolated reconstructions.Comment: 4 pages, 3 figure
Ocean surface current retrieval using a non homogeneous Markov-switching multi-regime model
International audienceThis paper addresses the reconstruction of sea surface currents from satellite ocean sensing data. Whereas the classical surface currents derived from the SSH (Sea Surface Height) products are rather low space-time resolution fields (typically, 50 km and 12-day actual space-time grid resolution), we investigate the extent to which we can retrieve sea surface currents at higher resolution using daily SST (Sea Surface Temperature) satellite observations. State-of-the-art methods, which exploit classical optical flow schemes or nonlinear regression techniques, do not provide satisfactory results due to the space-time variabilities of the relationships between the SST and the sea surface current. Motivated by our recent joint SST-SSH identification of characterization of upper ocean dynamical modes, we here show that a multi-regime model, formally stated as a Markov-switching latent class regression model, provides a relevant model to capture the above-mentioned variabilities and reconstruct SST-driven sea surface currents. The considered case study within the Agulhas current demonstrates that our model retrieves high-resolution space-time details which cannot be resolved by the classical SSH-derived products
Modeling processes asymmetries with Laplace Moving Average.
Many records in environmental science exhibit asymmetries: for example in shallow water and with variable bathymetry, the sea wave time series shows front-back asymmetries and different shapes for crests and troughs. In such situation, numerical models are available but are highly CPU-time consuming. A stochastic process aimed at modeling such asymmetries has already been proposed, the Laplace Moving Average process. The objective of this study is to propose a new estimator of the defining function in a non-parametric approach. Results based on a comprehensive numerical study will be shown in order to evaluate the performances of the proposed method
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