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

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

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

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

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

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. Université Bretagne Loire; FranciaFil: Tandeo, Pierre. Université Bretagne Loire; FranciaFil: Ailliot, Pierre. University of Western Brittany. Laboratoire de Mathématiques de Bretagne Atlantique; FranciaFil: Pulido, Manuel Arturo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Nordeste. Instituto de Modelado e Innovación Tecnológica. Universidad Nacional del Nordeste. Facultad de Ciencias Exactas Naturales y Agrimensura. Instituto de Modelado e Innovación Tecnológica; ArgentinaFil: Fablet, Ronan. Université Bretagne Loire; Franci

Non-parametric Ensemble Kalman methods for the inpainting of noisy dynamic textures

International audienceIn this work, we propose a novel non parametric method for the temporally consistent inpainting of dynamic texture sequences. The inpainting of texture image sequences is stated as a stochastic assimilation issue, for which a novel model-free and data-driven Ensemble Kalman method is introduced. Our model is inspired by the Analog Ensemble Kalman Filter (AnEnKF) recently proposed for the assimilation of geophysical space-time dynamics, where the physical model is replaced by the use of statistical analogs or nearest neighbours. Such a non-parametric framework is of key interest for image processing applications, as prior models are seldom available in general. We present experimental evidence for real dynamic texture that using only a catalog database of historical data and without having any assumption on the model, the proposed method provides relevant dynamically-consistent interpolation and outperforms the classical parametric (autoregressive) dynamical prior

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