Justin Winokur

Global sensitivity analysis in an ocean general circulation model: a sparse spectral projection approach

Polynomial chaos (PC) expansions are used to propagate parametric uncertainties in ocean global circulation model. The computations focus on short-time, high-resolution simulations of the Gulf of Mexico, using the hybrid coordinate ocean model, with wind stresses corresponding to hurricane Ivan. A sparse quadrature approach is used to determine the PC coefficients which provides a detailed representation of the stochastic model response. The quality of the PC representation is first examined through a systematic refinement of the number of resolution levels. The PC representation of the stochastic model response is then utilized to compute distributions of quantities of interest (QoIs) and to analyze the local and global sensitivity of these QoIs to uncertain parameters. Conclusions are finally drawn regarding limitations of local perturbations and variance-based assessment and concerning potential application of the present methodology to inverse problems and to uncertainty management.

A priori testing of sparse adaptive polynomial chaos expansions using an ocean general circulation model database

This work explores the implementation of an adaptive strategy to design sparse ensembles of oceanic simulations suitable for constructing polynomial chaos surrogates. We use a recently developed pseudo-spectral algorithm that is based on a direct application of the Smolyak sparse grid formula and that allows the use of arbitrary admissible sparse grids. The adaptive algorithm is tested using an existing simulation database of the oceanic response to Hurricane Ivan in the Gulf of Mexico. The a priori tests demonstrate that sparse and adaptive pseudo-spectral constructions lead to substantial savings over isotropic sparse sampling in the present setting.

Bayesian Inference of Drag Parameters Using AXBT Data from Typhoon Fanapi

AbstractThe authors introduce a three-parameter characterization of the wind speed dependence of the drag coefficient and apply a Bayesian formalism to infer values for these parameters from airborne expendable bathythermograph (AXBT) temperature data obtained during Typhoon Fanapi. One parameter is a multiplicative factor that amplifies or attenuates the drag coefficient for all wind speeds, the second is the maximum wind speed at which drag coefficient saturation occurs, and the third is the drag coefficients rate of change with increasing wind speed after saturation. Bayesian inference provides optimal estimates of the parameters as well as a non-Gaussian probability distribution characterizing the uncertainty of these estimates. The efficiency of this approach stems from the use of adaptive polynomial expansions to build an inexpensive surrogate for the high-resolution numerical model that couples simulated winds to the oceanic temperature data, dramatically reducing the computational burden of the M...

Development of a reduced model of formation reactions in Zr-Al nanolaminates

A computational model of anaerobic reactions in metallic multilayered systems with an equimolar composition of zirconium and aluminum is developed. The reduced reaction formalism of M. Salloum and O. M. Knio, Combust. Flame 157(2): 288–295 (2010) is adopted. Attention is focused on quantifying intermixing rates based on experimental measurements of uniform ignition as well as measurements of self-propagating front velocities. Estimates of atomic diffusivity are first obtained based on a regression analysis. A more elaborate Bayesian inference formalism is then applied in order to assess the impact of uncertainties in the measurements, potential discrepancies between predictions and observations, as well as the sensitivity of predictions to inferred parameters. Intermixing rates are correlated in terms of a composite Arrhenius law, which exhibits a discontinuity around the Al melting temperature. Analysis of the predictions indicates that Arrhenius parameters inferred for the low-temperature branch lie wit...

Sparse Pseudo Spectral Projection Methods with Directional Adaptation for Uncertainty Quantification

We investigate two methods to build a polynomial approximation of a model output depending on some parameters. The two approaches are based on pseudo-spectral projection (PSP) methods on adaptively constructed sparse grids, and aim at providing a finer control of the resolution along two distinct subsets of model parameters. The control of the error along different subsets of parameters may be needed for instance in the case of a model depending on uncertain parameters and deterministic design variables. We first consider a nested approach where an independent adaptive sparse grid PSP is performed along the first set of directions only, and at each point a sparse grid is constructed adaptively in the second set of directions. We then consider the application of aPSP in the space of all parameters, and introduce directional refinement criteria to provide a tighter control of the projection error along individual dimensions. Specifically, we use a Sobol decomposition of the projection surpluses to tune the sparse grid adaptation. The behavior and performance of the two approaches are compared for a simple two-dimensional test problem and for a shock-tube ignition model involving 22 uncertain parameters and 3 design parameters. The numerical experiments indicate that whereas both methods provide effective means for tuning the quality of the representation along distinct subsets of parameters, PSP in the global parameter space generally requires fewer model evaluations than the nested approach to achieve similar projection error. In addition, the global approach is better suited for generalization to more than two subsets of directions.

Quantifying initial and wind forcing uncertainties in the Gulf of Mexico

This study aims at analyzing the combined impact of uncertainties in initial conditions and wind forcing fields in ocean general circulation models (OGCM) using polynomial chaos (PC) expansions. Empirical orthogonal functions (EOF) are used to formulate both spatial perturbations to initial conditions and space-time wind forcing perturbations, namely in the form of a superposition of modal components with uniformly distributed random amplitudes. The forward deterministic HYbrid Coordinate Ocean Model (HYCOM) is used to propagate input uncertainties in the Gulf of Mexico (GoM) in spring 2010, during the Deepwater Horizon oil spill, and to generate the ensemble of model realizations based on which PC surrogate models are constructed for both localized and field quantities of interest (QoIs), focusing specifically on sea surface height (SSH) and mixed layer depth (MLD). These PC surrogate models are constructed using basis pursuit denoising methodology, and their performance is assessed through various statistical measures. A global sensitivity analysis is then performed to quantify the impact of individual modes as well as their interactions. It shows that the local SSH at the edge of the GoM main current—the Loop Current—is mostly sensitive to perturbations of the initial conditions affecting the current front, whereas the local MLD in the area of the Deepwater Horizon oil spill is more sensitive to wind forcing perturbations. At the basin scale, the SSH in the deep GoM is mostly sensitive to initial condition perturbations, while over the shelf it is sensitive to wind forcing perturbations. On the other hand, the basin MLD is almost exclusively sensitive to wind perturbations. For both quantities, the two sources of uncertainty have limited interactions. Finally, the computations indicate that whereas local quantities can exhibit complex behavior that necessitates a large number of realizations, the modal analysis of field sensitivities can be suitably achieved with a moderate size ensemble.

Propagation of uncertainty and sensitivity analysis in an integral oil-gas plume model

We thank the two anonymous reviewers for their constructive suggestions which improve this manuscript. This work was made possible in part by a grant from BP/ The Gulf of Mexico Research Initiative, and by the Office of Naval Research, Award N00014-101-0498. J. Winokur and O. M. Knio were also supported in part by the U.S. Department of Energy (DOE), Office of Science, Office of Advanced Scientific Computing Research, under Award DE-SC0008789. This research was conducted in collaboration with and using the resources of the University of Miami Center for Computational Science. The model data are publicly available in the Gulf of Mexico Research Initiative Information and Data Cooperative (GRIIDC) repository (https://data. gulfresearchinitiative.org/data/R4.x265. 252:0002/).

Summary of the 2014 Sandia Verification and Validation Challenge Workshop

A discussion of the five responses to the 2014 Sandia Verification and Validation (VV some of the major themes are discussed. Finally, an encapsulation of the key contributions, the lessons learned, and advice for the future are presented.