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Languages : en
Pages : 44
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Book Description
Uncertainty quantificatio in climate models is challenged by the sparsity of the available climate data due to the high computational cost of the model runs. Another feature that prevents classical uncertainty analyses from being easily applicable is the bifurcative behavior in the climate data with respect to certain parameters. A typical example is the Meridional Overturning Circulation in the Atlantic Ocean. The maximum overturning stream function exhibits discontinuity across a curve in the space of two uncertain parameters, namely climate sensitivity and CO2 forcing. We develop a methodology that performs uncertainty quantificatio in the presence of limited data that have discontinuous character. Our approach is two-fold. First we detect the discontinuity location with a Bayesian inference, thus obtaining a probabilistic representation of the discontinuity curve location in presence of arbitrarily distributed input parameter values. Furthermore, we developed a spectral approach that relies on Polynomial Chaos (PC) expansions on each sides of the discontinuity curve leading to an averaged-PC representation of the forward model that allows efficient uncertainty quantification and propagation. The methodology is tested on synthetic examples of discontinuous data with adjustable sharpness and structure.
Author:
Publisher:
ISBN:
Category :
Languages : en
Pages : 44
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Book Description
Uncertainty quantificatio in climate models is challenged by the sparsity of the available climate data due to the high computational cost of the model runs. Another feature that prevents classical uncertainty analyses from being easily applicable is the bifurcative behavior in the climate data with respect to certain parameters. A typical example is the Meridional Overturning Circulation in the Atlantic Ocean. The maximum overturning stream function exhibits discontinuity across a curve in the space of two uncertain parameters, namely climate sensitivity and CO2 forcing. We develop a methodology that performs uncertainty quantificatio in the presence of limited data that have discontinuous character. Our approach is two-fold. First we detect the discontinuity location with a Bayesian inference, thus obtaining a probabilistic representation of the discontinuity curve location in presence of arbitrarily distributed input parameter values. Furthermore, we developed a spectral approach that relies on Polynomial Chaos (PC) expansions on each sides of the discontinuity curve leading to an averaged-PC representation of the forward model that allows efficient uncertainty quantification and propagation. The methodology is tested on synthetic examples of discontinuous data with adjustable sharpness and structure.
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Languages : en
Pages : 18
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Author: Alexander G. Kalmikov
Publisher:
ISBN:
Category : Climatic changes
Languages : en
Pages : 160
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Book Description
Quantifying uncertainty and error bounds is a key outstanding challenge in ocean state estimation and climate research. It is particularly difficult due to the large dimensionality of this nonlinear estimation problem and the number of uncertain variables involved. The "Estimating the Circulation and Climate of the Oceans" (ECCO) consortium has developed a scalable system for dynamically consistent estimation of global time-evolving ocean state by optimal combination of ocean general circulation model (GCM) with diverse ocean observations. The estimation system is based on the "adjoint method" solution of an unconstrained least-squares optimization problem formulated with the method of Lagrange multipliers for fitting the dynamical ocean model to observations. The dynamical consistency requirement of ocean state estimation necessitates this approach over sequential data assimilation and reanalysis smoothing techniques. In addition, it is computationally advantageous because calculation and storage of large covariance matrices is not required. However, this is also a drawback of the adjoint method, which lacks a native formalism for error propagation and quantification of assimilated uncertainty. The objective of this dissertation is to resolve that limitation by developing a feasible computational methodology for uncertainty analysis in dynamically consistent state estimation, applicable to the large dimensionality of global ocean models. Hessian (second derivative-based) methodology is developed for Uncertainty Quantification (UQ) in large-scale ocean state estimation, extending the gradient-based adjoint method to employ the second order geometry information of the model-data misfit function in a high-dimensional control space. Large error covariance matrices are evaluated by inverting the Hessian matrix with the developed scalable matrix-free numerical linear algebra algorithms. Hessian-vector product and Jacobian derivative codes of the MIT general circulation model (MITgcm) are generated by means of algorithmic differentiation (AD). Computational complexity of the Hessian code is reduced by tangent linear differentiation of the adjoint code, which preserves the speedup of adjoint checkpointing schemes in the second derivative calculation. A Lanczos algorithm is applied for extracting the leading rank eigenvectors and eigenvalues of the Hessian matrix. The eigenvectors represent the constrained uncertainty patterns. The inverse eigenvalues are the corresponding uncertainties. The dimensionality of UQ calculations is reduced by eliminating the uncertainty null-space unconstrained by the supplied observations. Inverse and forward uncertainty propagation schemes are designed for assimilating observation and control variable uncertainties, and for projecting these uncertainties onto oceanographic target quantities. Two versions of these schemes are developed: one evaluates reduction of prior uncertainties, while another does not require prior assumptions. The analysis of uncertainty propagation in the ocean model is time-resolving. It captures the dynamics of uncertainty evolution and reveals transient and stationary uncertainty regimes. The system is applied to quantifying uncertainties of Antarctic Circumpolar Current (ACC) transport in a global barotropic configuration of the MITgcm. The model is constrained by synthetic observations of sea surface height and velocities. The control space consists of two-dimensional maps of initial and boundary conditions and model parameters. The size of the Hessian matrix is 0(1010) elements, which would require 0(60GB) of uncompressed storage. It is demonstrated how the choice of observations and their geographic coverage determines the reduction in uncertainties of the estimated transport. The system also yields information on how well the control fields are constrained by the observations. The effects of controls uncertainty reduction due to decrease of diagonal covariance terms are compared to dynamical coupling of controls through off-diagonal covariance terms. The correlations of controls introduced by observation uncertainty assimilation are found to dominate the reduction of uncertainty of transport. An idealized analytical model of ACC guides a detailed time-resolving understanding of uncertainty dynamics. Keywords: Adjoint model uncertainty, sensitivity, posterior error reduction, reduced rank Hessian matrix, Automatic Differentiation, ocean state estimation, barotropic model, Drake Passage transport.
Author: Ralph C. Smith
Publisher: SIAM
ISBN: 1611973228
Category : Computers
Languages : en
Pages : 400
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Book Description
The field of uncertainty quantification is evolving rapidly because of increasing emphasis on models that require quantified uncertainties for large-scale applications, novel algorithm development, and new computational architectures that facilitate implementation of these algorithms. Uncertainty Quantification: Theory, Implementation, and Applications provides readers with the basic concepts, theory, and algorithms necessary to quantify input and response uncertainties for simulation models arising in a broad range of disciplines. The book begins with a detailed discussion of applications where uncertainty quantification is critical for both scientific understanding and policy. It then covers concepts from probability and statistics, parameter selection techniques, frequentist and Bayesian model calibration, propagation of uncertainties, quantification of model discrepancy, surrogate model construction, and local and global sensitivity analysis. The author maintains a complementary web page where readers can find data used in the exercises and other supplementary material.
Author: Michael J. P. Cullen
Publisher: Imperial College Press
ISBN: 1860949193
Category : Science
Languages : en
Pages : 274
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Book Description
This book counteracts the current fashion for theories of OC chaosOCO and unpredictability by describing a theory that underpins the surprising accuracy of current deterministic weather forecasts, and it suggests that further improvements are possible. The book does this by making a unique link between an exciting new branch of mathematics called OC optimal transportationOCO and existing classical theories of the large-scale atmosphere and ocean circulation. It is then possible to solve a set of simple equations proposed many years ago by Hoskins which are asymptotically valid on large scales, and use them to derive quantitative predictions about many large-scale atmospheric and oceanic phenomena. A particular feature is that the simple equations used have highly predictable solutions, thus suggesting that the limits of deterministic predictability of the weather may not yet have been reached. It is also possible to make rigorous statements about the large-scale behaviour of the atmosphere and ocean by proving results using these simple equations and applying them to the real system allowing for the errors in the approximation. There are a number of other titles in this field, but they do not treat this large-scale regime. Contents: The Governing Equations and Asymptotic Approximations to Them; Solution of the Semi-Geostrophic Equations in Plane Geometry; Solution of the Semi-Geostrophic Equations in More General Cases; Properties of Semi-Geostrophic Solutions; Application of Semi-Geostrophic Theory to the Predictability of atmospheric Flows. Readership: Researchers and graduate students in atmosphere/ocean dynamics with some mathematical background."
Author: Eric P. Chassignet
Publisher: Springer Science & Business Media
ISBN: 1402040288
Category : Science
Languages : en
Pages : 573
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Book Description
This volume covers a wide range of topics and summarizes our present knowledge in ocean modeling, ocean observing systems, and data assimilation. The Global Ocean Data Assimilation Experiment (GODAE) provides a framework for these efforts: a global system of observations, communications, modeling, and assimilation that will deliver regular, comprehensive information on the state of the oceans, engendering wide utility and availability for maximum benefit to the community.
Author: Henk A. Dijkstra
Publisher: Springer Science & Business Media
ISBN: 9401594503
Category : Science
Languages : en
Pages : 469
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Book Description
In this book, the methodology of dynamical systems theory is applied to investigate the physics of the global ocean circulation. Topics include the dynamics of the Gulf Stream in the Atlantic Ocean, the stability of the thermohaline circulation and the El Niño/Southern Oscillation phenomenon in the Tropical Pacific. On the other hand, the book also deals with the numerical methods for applying bifurcation analysis on large dimensional dynamical systems, with thousands or more degrees of freedom, which arise through discretization of ocean models. The novel approach in understanding the phenomena of climate variability is through a systematic analysis within a hierarchy of models using these techniques. In this way, a nice overview is obtained of the relations between the results of the different models within the hierarchy. Mechanistic description of the physics of the results is provided and, where possible, links with results of state-of-the-art models and observations are sought. The reader is expected to have a background in basic incompressible fluid dynamics and applied mathematics, although the level of the text is mixed and sometimes quite introductory. Each chapter is rather self-contained and many details of derivations are provided. The book is aimed at graduate students and researchers in meteorology, oceanography, and related fields who are interested in tackling fundamental problems in dynamical oceanography and climate dynamics.
Author: José Eduardo Souza De Cursi
Publisher: Springer Nature
ISBN: 3031470362
Category : Technology & Engineering
Languages : en
Pages : 282
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Book Description
This proceedings book covers a wide range of topics related to uncertainty analysis and its application in various fields of engineering and science. It explores uncertainties in numerical simulations for soil liquefaction potential, the toughness properties of construction materials, experimental tests on cyclic liquefaction potential, and the estimation of geotechnical engineering properties for aerogenerator foundation design. Additionally, the book delves into uncertainties in concrete compressive strength, bio-inspired shape optimization using isogeometric analysis, stochastic damping in rotordynamics, and the hygro-thermal properties of raw earth building materials. It also addresses dynamic analysis with uncertainties in structural parameters, reliability-based design optimization of steel frames, and calibration methods for models with dependent parameters. The book further explores mechanical property characterization in 3D printing, stochastic analysis in computational simulations, probability distribution in branching processes, data assimilation in ocean circulation modeling, uncertainty quantification in climate prediction, and applications of uncertainty quantification in decision problems and disaster management. This comprehensive collection provides insights into the challenges and solutions related to uncertainty in various scientific and engineering contexts.
Author: Aike Beckmann
Publisher: World Scientific
ISBN: 1848168241
Category : Science
Languages : en
Pages : 342
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Book Description
This book offers a comprehensive overview of the models and methods employed in the rapidly advancing field of numerical ocean circulation modeling. For those new to the field, concise reviews of the equations of oceanic motion, sub-grid-scale parameterization, and numerical approximation techniques are presented and four specific numerical models, chosen to span the range of current practice, are described in detail. For more advanced users, a suite of model test problems is developed to illustrate the differences among models, and to serve as a first stage in the quantitative evaluation of future algorithms. The extensive list of references makes this book a valuable text for both graduate students and postdoctoral researchers in the marine sciences and in related fields such as meteorology, and climate and coupled biogeochemical modeling.
Author: Haraldur Olafsson
Publisher: Elsevier
ISBN: 0128157100
Category : Science
Languages : en
Pages : 366
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Book Description
Uncertainties in Numerical Weather Prediction is a comprehensive work on the most current understandings of uncertainties and predictability in numerical simulations of the atmosphere. It provides general knowledge on all aspects of uncertainties in the weather prediction models in a single, easy to use reference. The book illustrates particular uncertainties in observations and data assimilation, as well as the errors associated with numerical integration methods. Stochastic methods in parameterization of subgrid processes are also assessed, as are uncertainties associated with surface-atmosphere exchange, orographic flows and processes in the atmospheric boundary layer. Through a better understanding of the uncertainties to watch for, readers will be able to produce more precise and accurate forecasts. This is an essential work for anyone who wants to improve the accuracy of weather and climate forecasting and interested parties developing tools to enhance the quality of such forecasts. - Provides a comprehensive overview of the state of numerical weather prediction at spatial scales, from hundreds of meters, to thousands of kilometers - Focuses on short-term 1-15 day atmospheric predictions, with some coverage appropriate for longer-term forecasts - Includes references to climate prediction models to allow applications of these techniques for climate simulations
