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Search Results: 1 - 10 of 167866 matches for " E. Foufoula-Georgiou "
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Chaotic behavior in the flow along a wedge modeled by the Blasius equation
B. Basu, E. Foufoula-Georgiou,A. S. Sharma
Nonlinear Processes in Geophysics (NPG) , 2011,
Abstract: The Blasius equation describes the properties of steady-state two dimensional boundary layer forming over a semi-infinite plate parallel to a unidirectional flow field. The flow is governed by a modified Blasius equation when the surface is aligned along the flow. In this paper, we demonstrate using numerical solution, that as the wedge angle increases, bifurcation occurs in the nonlinear Blasius equation and the dynamics becomes chaotic leading to non-convergence of the solution once the angle exceeds a critical value of 22°. This critical value is found to be in agreement with experimental results showing the development of shock waves in the medium and also with analytical results showing multiple solutions for wedge angles exceeding a critical value. Finally, we provide a derivation of the equation governing the boundary layer flow for wedge angles exceeding the critical angle at the onset of chaos.
Variational Data Assimilation via Sparse Regularization
A. M. Ebtehaj,M. Zupanski,G. Lerman,E. Foufoula-Georgiou
Physics , 2013, DOI: 10.3402/tellusa.v66.21789
Abstract: 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 $\ell_{1}$-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.
GPM Draft Science Implementation Plan Ground Validation Chapter
S. Yuter,R. Houze,V. Chandrasekar,E. Foufoula-Georgiou,M. Hagen,R. Johnson,D. Kingsmill,R. Lawrence,F. Marks,S. Rutledge,J. Weinman
Physics , 2002,
Abstract: The validation of NASA Global Precipitation Mission (GPM) satellite precipitation products is important for their credibility and utility within the larger community. This document defines GPM ground validation scientific objectives and several programmatic components for meeting those objectives. Multi-year, multi-sensor ground-based observation programs in a few locations are proposed to generate local observation products and global error covariance products. Focused measurement programs utilizing aircraft, ships, and ground-based measurements would fill in geographic and scientific gaps not addressed by the multi-year observing programs.
Variational Downscaling, Fusion and Assimilation of Hydrometeorological States via Regularized Estimation
Ardeshir Mohammad Ebtehaj,Efi Foufoula-Georgiou
Physics , 2012, DOI: 10.1002/wrcr.20424
Abstract: Improved estimation of hydrometeorological states from down-sampled observations and background model forecasts in a noisy environment, has been a subject of growing research in the past decades. Here, we introduce a unified framework that ties together the problems of downscaling, data fusion and data assimilation as ill-posed inverse problems. This framework seeks solutions beyond the classic least squares estimation paradigms by imposing proper regularization, which are constraints consistent with the degree of smoothness and probabilistic structure of the underlying state. We review relevant regularization methods in derivative space and extend classic formulations of the aforementioned problems with particular emphasis on hydrologic and atmospheric applications. Informed by the statistical characteristics of the state variable of interest, the central results of the paper suggest that proper regularization can lead to a more accurate and stable recovery of the true state and hence more skillful forecasts. In particular, using the Tikhonov and Huber regularization in the derivative space, the promise of the proposed framework is demonstrated in static downscaling and fusion of synthetic multi-sensor precipitation data, while a data assimilation numerical experiment is presented using the heat equation in a variational setting.
Transport on river networks: A dynamical approach
Ilya Zaliapin,Efi Foufoula-Georgiou,Michael Ghil
Physics , 2009, DOI: 10.1029/2009JF00128
Abstract: This study is motivated by problems related to environmental transport on river networks. We establish statistical properties of a flow along a directed branching network and suggest its compact parameterization. The downstream network transport is treated as a particular case of nearest-neighbor hierarchical aggregation with respect to the metric induced by the branching structure of the river network. We describe the static geometric structure of a drainage network by a tree, referred to as the static tree, and introduce an associated dynamic tree that describes the transport along the static tree. It is well known that the static branching structure of river networks can be described by self-similar trees (SSTs); we demonstrate that the corresponding dynamic trees are also self-similar. We report an unexpected phase transition in the dynamics of three river networks, one from California and two from Italy, demonstrate the universal features of this transition, and seek to interpret it in hydrological terms.
Estimating Intermittency Exponent in Neutrally Stratified Atmospheric Surface Layer Flows: A Robust Framework based on Magnitude Cumulant and Surrogate Analyses
Sukanta Basu,Efi Foufoula-Georgiou,Bruno Lashermes,Alain Arneodo
Physics , 2007, DOI: 10.1063/1.2786001
Abstract: This study proposes a novel framework based on magnitude cumulant and surrogate analyses to reliably detect and estimate the intermittency coefficient from short-length coarse-resolution turbulent time series. Intermittency coefficients estimated from a large number of neutrally stratified atmospheric surface layer turbulent series from various field campaigns are shown to remarkably concur with well-known laboratory experimental results. In addition, surrogate-based hypothesis testing significantly reduces the likelihood of detecting a spurious non-zero intermittency coefficient from non-intermittent series. The discriminatory power of the proposed framework is promising for addressing the unresolved question of how atmospheric stability affects the intermittency properties of boundary layer turbulence.
On evaluation of ShARP passive rainfall retrievals over snow-covered land surfaces and coastal zones
Ardeshir M. Ebtehaj,Rafael L. Bras,Efi Foufoula-Georgiou
Physics , 2015,
Abstract: For precipitation retrievals over land, using satellite measurements in microwave bands, it is important to properly discriminate the weak rainfall signals from strong and highly variable background surface emission. Traditionally, land rainfall retrieval methods often rely on a weak signal of rainfall scattering on high-frequency channels (85 GHz) and make use of empirical thresholding and regression-based techniques. Due to the increased ground surface signal interference, precipitation retrieval over radiometrically complex land surfaces, especially over snow-covered lands, deserts and coastal areas, is of particular challenge for this class of retrieval techniques. This paper evaluates the results by the recently proposed Shrunken locally linear embedding Algorithm for Retrieval of Precipitation (ShARP), over a radiometrically complex terrain and coastal areas using the data provided by the Tropical Rainfall Measuring Mission (TRMM) satellite. To this end, the ShARP retrieval experiments are performed over a region in Southeast Asia, partly covering the Tibetan Highlands, Himalayas, Ganges-Brahmaputra-Meghna river basins and its delta. We elucidate promising results by ShARP over snow covered land surfaces and at the vicinity of coastlines, in comparison with the land rainfall retrievals of the standard TRMM-2A12 product. Specifically, using the TRMM-2A25 radar product as a reference, we provide evidence that the ShARP algorithm can significantly reduce the rainfall over estimation due to the background snow contamination and markedly improve detection and retrieval of rainfall at the vicinity of coastlines. During the calendar year 2013, we demonstrate that over the study domain the root mean squared difference can be reduced up to 38% annually, while the reduction can reach up to 70% during the cold months.
Synthetic Turbulence, Fractal Interpolation and Large-Eddy Simulation
Sukanta Basu,Efi Foufoula-Georgiou,Fernando Porté-Agel
Physics , 2003, DOI: 10.1103/PhysRevE.70.026310
Abstract: Fractal Interpolation has been proposed in the literature as an efficient way to construct closure models for the numerical solution of coarse-grained Navier-Stokes equations. It is based on synthetically generating a scale-invariant subgrid-scale field and analytically evaluating its effects on large resolved scales. In this paper, we propose an extension of previous work by developing a multiaffine fractal interpolation scheme and demonstrate that it preserves not only the fractal dimension but also the higher-order structure functions and the non-Gaussian probability density function of the velocity increments. Extensive a-priori analyses of atmospheric boundary layer measurements further reveal that this Multiaffine closure model has the potential for satisfactory performance in large-eddy simulations. The pertinence of this newly proposed methodology in the case of passive scalars is also discussed.
Shrunken Locally Linear Embedding for Passive Microwave Retrieval of Precipitation
Ardeshir Mohammad Ebtehaj,Rafael Luis Bras,Efi Foufoula-Georgiou
Physics , 2014, DOI: 10.1109/TGRS.2014.2382436
Abstract: This paper introduces a new Bayesian approach to the inverse problem of passive microwave rainfall retrieval. The proposed methodology relies on a regularization technique and makes use of two joint dictionaries of coincidental rainfall profiles and their corresponding upwelling spectral radiative fluxes. A sequential detection-estimation strategy is adopted, which basically assumes that similar rainfall intensity values and their spectral radiances live close to some sufficiently smooth manifolds with analogous local geometry. The detection step employs a nearest neighborhood classification rule, while the estimation scheme is equipped with a constrained shrinkage estimator to ensure stability of retrieval and some physical consistency. The algorithm is examined using coincidental observations of the active precipitation radar (PR) and passive microwave imager (TMI) on board the Tropical Rainfall Measuring Mission (TRMM) satellite. We present promising results of instantaneous rainfall retrieval for some tropical storms and mesoscale convective systems over ocean, land, and coastal zones. We provide evidence that the algorithm is capable of properly capturing different storm morphologies including high intensity rain-cells and trailing light rainfall, especially over land and coastal areas. The algorithm is also validated at an annual scale for calendar year 2013 versus the standard (version 7) radar (2A25) and radiometer (2A12) rainfall products of the TRMM satellite.
Transport and Vulnerability in River Deltas: A Graph-Theoretic Approach
Alejandro Tejedor,Anthony Longjas,Ilya Zaliapin,Efi Foufoula-Georgiou
Physics , 2014,
Abstract: Maintaining a sustainable socio-ecological state of a river delta requires delivery of material and energy fluxes to its body and coastal zone in a way that avoids malnourishment that would compromise system integrity. We present a quantitative framework for studying delta topology and transport based on representation of a deltaic system by a rooted directed acyclic graph. Applying results from spectral graph theory allows systematic identification of the upstream and downstream subnetworks for a given vertex, computing steady flux propagation in the network, and finding partition of the flow at any channel among the downstream channels. We use this framework to construct vulnerability maps that quantify the relative change of sediment and water delivery to the shoreline outlets in response to possible perturbations in hundreds of upstream links. This enables us to evaluate which links hotspots and what management scenarios would most influence flux delivery to the outlets. The results can be used to examine local or spatially distributed delta interventions and develop a system approach to delta management.
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