W. Carlisle Thacker

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.

Estimation of salinity profiles in the upper ocean

A new algorithm is presented for estimating salinity profiles in the upper ocean from measurements of temperature profiles and surface salinity. In application to the eastern tropical Pacific the method replicates a large fraction of the variability of salinity in the upper few tens of meters and provides modest to substantial improvement at nearly all levels. Estimated salinity profiles are able to characterize barrier layers, regions formed by a halocline within the thermal mixed layer. The rms error of geopotential height calculations based on estimated salinity profiles is reduced more than 50% by this method relative to methods not using surface salinity. Even without the surface salinity measurement some reduction of error in geopotential heights can be obtained relative to previous methods.

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...

Drag Parameter Estimation Using Gradients and Hessian from a Polynomial Chaos Model Surrogate

A variational inverse problem is solved using polynomial chaos expansions to infer several critical variables in the Hybrid Coordinate Ocean Model’s (HYCOM’s) wind drag parameterization. This alternative to the Bayesian inference approach in Sraj et al. avoids the complications of constructing the full posterior with Markov chain Monte Carlo sampling. It focuses instead on identifying the center and spread of the posterior distribution. The present approach leverages the polynomial chaos series to estimate, at very little extra cost, the gradients and Hessian of the cost function during minimization. The Hessian’s inverse yields an estimate of the uncertainty in the solution when the latter’s probability density is approximately Gaussian. The main computational burden is an ensemble of realizations to build the polynomial chaos expansion; no adjoint code or additional forward model runs are needed once the series is available. The ensuing optimal parameters are compared to those obtained in Sraj et al. where the full posterior distribution was constructed. The similarities and differences between the new methodology and a traditional adjoint-based calculation are discussed.

A framework to quantify uncertainty in simulations of oil transport in the ocean

This research was made possible in part by a grant from BP/The Gulf of Mexico Research Initiative to the Deep-C and CARTHE Consortia, by the Office of Naval Research, award N00014-101-0498, and by the US Department of the Interior, Bureau of Ocean Energy Management under the cooperative agreement MC12AC00019. R. Goncalves acknowledges support by the Brazilian Ministry of Science, Technology and Innovation (CNPq-Council for Scientific and Technological Development) through a PHD scholarship from the Science Without Borders program, grant 202263/2012-6. O. Knio acknowledges partial support from the US Department of Energy, 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 outputs of the DeepC Oil Model used here are publicly available through the Gulf of Mexico Research Initiative Information & Data Cooperative (GRIIDC). [Available at https://data.gulfresearchinitiative.org/data/R1.x138.077:0026.]

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/).