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.United States. Office of Naval Research (award N00014-101-0498)United States. Dept. of Energy. Office of Advanced Scientific Computing Research (award numbers DE-SC0007020, DE-SC0008789, and DE-SC0007099)Gulf of Mexico Research Initiative (contract numbers SA1207GOMRI005 (CARTHE) and SA12GOMRI008 (DEEP-C)

Reconstruction of Submesoscale Velocity Field from Surface Drifters

Abstract The extensive drifter deployment during the Lagrangian Submesoscale Experiment (LASER) provided observations of the surface velocity field in the northern Gulf of Mexico with high resolution in space and time. Here, we estimate the submesoscale velocity field sampled by those drifters using a procedure that statistically interpolates these data both spatially and temporally. Because the spacing of the drifters evolves with the flow, causing the resolution that they provide to vary in space and time, it is important to be able to characterize where and when the estimated velocity field is more or less accurate, which we do by providing fields of interpolation errors. Our interpolation uses a squared-exponential covariance function characterizing correlations in latitude, longitude, and time. Two novelties in our approach are 1) the use of two scales of variation per dimension in the covariance function and 2) allowing the data to determine these scales along with the appropriate amplitude of observational noise at these scales. We present the evolution of the reconstructed velocity field along with maps of relative vorticity, horizontal divergence, and lateral strain rate. The reconstructed velocity field exhibits horizontal length scales of 0.4–3.5 km and time scales of 0.6–3 h, and features with convergence up to 8 times the planetary vorticity f, lateral strain rate up to 10f, and relative vorticity up to 13f. Our results point to the existence of a vigorous and substantial ageostrophic circulation in the submesoscale range

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

Abstract 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

Variational approaches on discontinuity localization and field estimation in sea surface temperature and soil moisture

Some applications in remote sensing require estimating a field containing a discontinuity whose exact location is a priori unknown. Such fields of interest include sea surface temperature in oceanography and soil moisture in hydrology. For the former, oceanic fronts form a temperature discontinuity, while in the latter sharp changes exist across the interface between soil types. To complicate the estimation process, remotely sensed measurements often exhibit regions of missing observations due to occlusions such as cloud cover. Similarly, water surface and ground-based sensors usually provide only an incomplete set of measurements. Traditional methods of interpolation and smoothing for estimating the fields from such potentially sparse measurements often blur across the discontinuities in the field

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

An uncertainty quantification framework is developed for the DeepC Oil Model based on a nonintrusive polynomial chaos method. This allows the model's output to be presented in a probabilistic framework so that the model's predictions reflect the uncertainty in the model's input data. The new capability is illustrated by simulating the far‐field dispersal of oil in a Deepwater Horizon blowout scenario. The uncertain input consisted of ocean current and oil droplet size data and the main model output analyzed is the ensuing oil concentration in the Gulf of Mexico. A 1331 member ensemble was used to construct a surrogate for the model which was then mined for statistical information. The mean and standard deviations in the oil concentration were calculated for up to 30 days, and the total contribution of each input parameter to the model's uncertainty was quantified at different depths. Also, probability density functions of oil concentration were constructed by sampling the surrogate and used to elaborate probabilistic hazard maps of oil impact. The performance of the surrogate was constantly monitored in order to demarcate the space‐time zones where its estimates are reliable. Key Points: Uncertainties in currents and oil buoyancy were characterized using three random input variables The dominant contributor to oil concentration uncertainties is identified via variance analysis Probabilistic hazard maps of oil impact are constructed based on the input uncertaint

Bayesian Inference of Drag Parameters Using AXBT Data from Typhoon Fanapi

Abstract The 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 coefficient's 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 Markov chain Monte Carlo sampling. These results indicate that the most likely values for the drag coefficient saturation and the corresponding wind speed are about 2.3 × 10−3 and 34 m s−1, respectively; the data were not informative regarding the drag coefficient behavior at higher wind speeds

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