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.

AbstractOcean currents are an important consideration throughout the life cycle of the many offshore projects. These currents are complex, three dimensional, dynamic and as yet poorly characterized in a statistical sense. Numerical ocean circulation models are increasingly sophisticated and are beginning to capture the structure and variability of complex ocean current systems. The starting point for model-based characterization of currents is a long time series of model outputs obtained at high spatial and temporal resolution. There are an ever-increasing number of model products, but it is not clear how to identify suitable products for a given application. Frequently, a familiar product is chosen that may not be the best choice. Here, we present an alternative approach wherein a collection of model runs, referred to as an ensemble, is used to estimate ocean current statistics at points of interest. Unlike other ensemble methods where the ensemble is used to estimate the statistics directly, we use the ensemble to construct a surrogate ocean model or an emulator using polynomial expansions. This emulator is computationally inexpensive to run and is used to sample the model outputs for large numbers of model inputs to generate full probability distributions of the model state, which can then be used to derive statistics required for design criteria. We have used the above technique to build an emulator for a numerical circulation model of the Gulf of Mexico. We present statistics of the Loop Current derived from this approach and briefly compare it with statistics obtained from measurements and other available long time-series of model outputs. Probability distributions for a sample point in the vicinity of the Loop Current are presented. It is shown that the technique can provide robust statistics and complements existing techniques.

Polynomial Chaos (PC) methods are used to quantify the impacts of initial conditions uncertainties on oceanic forecasts of the Gulf of Mexico circulation. Empirical Orthogonal Functions are used as initial conditions perturbations with their modal amplitudes considered as uniformly distributed uncertain random variables. These perturbations impact primarily the Loop Current system and several frontal eddies located in its vicinity. A small ensemble is used to sample the space of the modal amplitudes and to construct a surrogate for the evolution of the model predictions via a nonintrusive Galerkin projection. The analysis of the surrogate yields verification measures for the surrogate's reliability and statistical information for the model output. A variance analysis indicates that the sea surface height predictability in the vicinity of the Loop Current is limited to about 20 days.

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/).

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 spacetime zones where its estimates are reliable.

We give an overview of four different ensemble-based techniques for uncertainty quantification and illustrate their application in the context of oil plume simulations. These techniques share the common paradigm of constructing a model proxy that efficiently captures the functional dependence of the model output on uncertain model inputs. This proxy is then used to explore the space of uncertain inputs using a large number of samples, so that reliable estimates of the model's output statistics can be calculated. Three of these techniques use polynomial chaos (PC) expansions to construct the model proxy, but they differ in their approach to determining the expansions' coefficients; the fourth technique uses Gaussian Process Regression (GPR). An integral plume model for simulating the Deepwater Horizon oil-gas blowout provides examples for illustrating the different techniques. A Monte Carlo ensemble of 50,000 model simulations is used for gauging the performance of the different proxies. The examples illustrate how regression-based techniques can outperform projection-based techniques when the model output is noisy. They also demonstrate that robust uncertainty analysis can be performed at a fraction of the cost of the Monte Carlo calculation.

When quantifying the uncertainty of the response of a computationally costly oceanographic or meteorological model stemming from the uncertainty of its inputs, practicality demands getting the most information using the fewest simulations. It is widely recognized that, by interpolating the results of a small number of simulations, results of additional simulations can be inexpensively approximated to provide a useful estimate of the variability of the response. Even so, as computing the simulations to be interpolated remains the biggest expense, the choice of these simulations deserves attention. When making this choice, two requirement should be considered: (i) the nature of the interpolation and (ii) the available information about input uncertainty. Examples comparing polynomial interpolation and Gaussian process interpolation are presented for three different views of input uncertainty. (C) 2015 Elsevier Ltd. All rights reserved.

Predictions of the rate of accumulation of anthropogenic carbon dioxide in the Pacific Ocean near 32°S and 150°W based on the P16 surveys of 1991 and 2005 and on the P06 surveys of 1992 and 2003 underestimate the amount found in the P06 survey of 2009-2010, suggesting an increasing uptake rate. Assuming the accumulation rate to be constant over the two decades, analyses using all five surveys lead to upward revision of the rates based only on the first four. On the other hand, accumulation rates estimated for 2003-2010 are significantly greater than those for 1991-2003, again suggesting an increasing uptake rate. In addressing this question it is important to acknowledge the limitations of the repeat hydrography and consequent uncertainties of estimated accumulation rates.

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.

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 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 M...

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.

Regression-based methods used for estimating the rate of increase of anthropogenic CO2 in the ocean are reviewed and guidelines for improvement are presented. Following these guidelines leads to a local two-regression method, the first regression accounting for changes in oceanic carbon due to natural variability and the second regression associating the remaining systematic temporal variability with the anthropogenic signal to quantify the rate of accumulation. While a formal measure of the accumulation rate's uncertainty is provided by the standard error of the second regression's slope parameter, both the available data's limited ability to characterize carbon's natural variability in the absence of any anthropogenic contribution and the choice of regressors to account for that variability present significant uncertainties that are less easily quantified. An attractive feature of the method is its applicability to data other than those from repeated hydrographic surveys, such as might be provided by appropriately instrumented profiling floats.

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.

The method of polynomial chaos expansions is illustrated by showing how uncertainties in boundary conditions specifying the flow from the Caribbean Sea into the Gulf of Mexico manifest as uncertainties in a model's simulation of the Gulfs surface elevation field. The method, which has been used for a variety of engineering applications, is explained within an oceanographic context and its advantages and disadvantages are discussed. The method's utility requires that the spatially and temporally varying uncertainties of the inflow be characterized by a small number of independent random variables, which here correspond to amplitudes of spatiotemporal modes inferred from an available boundary climatology. (C) 2011 Elsevier Ltd. All rights reserved.

We assess and compare four sequential data assimilation methods developed for HYCOM in an identical twin experiment framework. The methods considered are Multi-variate Optimal Interpolation (MVOI), Ensemble Optimal Interpolation (EnOI), the fixed basis version of the Singular Evolutive Extended Kalman Filter (SEEK) and the Ensemble Reduced Order Information Filter (EnROIF). All methods can be classified as statistical interpolation but differ mainly in how the forecast error covariances are modeled. Surface elevation and temperature data sampled from an 1/12 degrees Gulf of Mexico HYCOM simulation designated as the truth are assimilated into an identical model starting from an erroneous initial state, and convergence of assimilative runs towards the truth is tracked. Sensitivity experiments are first performed to evaluate the impact of practical implementation choices such as the state vector structure, initialization procedures, correlation scales, covariance rank and details of handling multivariate datasets, and to identify an effective configuration for each assimilation method. The performance of the methods are then compared by examining the relative convergence of the assimilative runs towards the truth. All four methods show good skill and are able to enhance consistency between the assimilative and truth runs in both observed and unobserved model variables. Prediction errors in observed variables are typically less than the errors specified for the observations, and the differences between the assimilated products are small compared to the observation errors. For unobserved variables, RMS errors are reduced by 50% relative to a non-assimilative run and differ between schemes on average by about 5%. Dynamical consistency between the updated state space variables in the data assimilation algorithm, and the data adequately sampling significant dynamical features are the two crucial components for reliable predict:ions. The experiments presented here suggest that practical implementation details can have at least as much an impact on the accuracy of the assimilated product as the choice of assimilation technique itself. We also present a discussion of the numerical implementation and the computational requirements for the use of these methods in large scale applications. (C) 2011 Elsevier Ltd. All rights reserved.

The Deep Water Horizon well blowout on April 20th 2010 discharged between 40,000-1.2 million tons of crude oil into the Gulf of Mexico. In order to understand the fate and impact of the discharged oil, particularly on the environmentally sensitive Florida Keys region, we have implemented a multi-component application which consists of many individual tasks that utilize a distributed set of computational and data management resources. The application consists of two 3D ocean circulation models of the Gulf and South Florida and a 3D oil spill model. The ocean models used here resolve the Gulf at 2 km and the South Florida region at 900 m. This high resolution information on the ocean state is then integrated with the oil model to track the fate of approximately 10 million oil particles. These individual components execute as MPI based parallel applications on a 576 core IBM Power 5 cluster and a 5040 core Linux cluster, both operated by the Center for Computational Science, University of Miami. The data and workflow between is handled by means of a custom distributed software framework built around the Open Project for Networked Data Access Protocol (OPeNDAP). In this paper, we present this application as an example of Many Task Computing, report on the execution characteristics of this application, and discuss the challenges presented by the many task distributed workflow involving heterogeneous components. The application is a typical example from the ocean modeling and forecasting field and imposes soft timeliness and output quality constraints on top of the traditional performance requirements.

The empirical relationship between salinity and temperature in the South Atlantic is quantified with the aid of local regression. To capture the spatial character of the TS relationship, models are fitted to data for each point on a three-dimensional grid with spacing of 1 degrees in latitude, 2 degrees in longitude, and 25 dbar in the vertical. To ensure sufficient data for statistical reliability each fit is to data from a region extending over several grid points weighted so that more remote data exert less influence than those closer to the target grid point. Both temperature and its square are used as regressors to capture the curvature seen in TS plots, and latitude and longitude are used to capture systematic spatial variations over the fitting regions. In addition to using statistics of residuals to characterize how well the models fit the data, errors for data not used in fitting are examined to verify the models' abilities to simulate independent data. The best model overall for the entire region at all depths is quadratic in temperature and linear in longitude and latitude.