Mohamed Iskandarani

A three-dimensional spectral element model for the solution of the hydrostatic primitive equations

We present a spectral element model to solve the hydrostatic primitive equations governing large-scale geophysical flows. The highlights of this new model include unstructured grids, dual h–p paths to convergence, and good scalability characteristics on present day parallel computers including Beowulf-class systems. The behavior of the model is assessed on three process-oriented test problems involving wave propagation, gravitational adjustment, and nonlinear flow rectification, respectively. The first of these test problems is a study of the convergence properties of the model when simulating the linear propagation of baroclinic Kelvin waves. The second is an intercomparison of spectral element and finite-difference model solutions to the adjustment of a density front in a straight channel. Finally, the third problem considers the comparison of model results to measurements obtained from a laboratory simulation of flow around a submarine canyon. The aforementioned tests demonstrate the good performance of the model in the idealized/processoriented limits. 2003 Elsevier Science B.V. All rights reserved.

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.

Global Modelling of the Ocean and Atmosphere Using the Spectral Element Method

ABSTRACT The use of spectral methods now has a long history in global atmospheric modelling wherein the attractive properties of Fourier series on spheres, including higher-order convergence rates and efficient implementation via the transform method, have proven advantageous. Partially offsetting these advantages, however, are several competing disadvantages. Two of these, the appearance of Gibbs oscillations for localized processes (e.g., orographic interactions) and the difficulty of mapping spectral techniques onto parallel computer architectures, are inherent to the global nature of these techniques. A third drawback, the restriction of these methods to regular geometries, has severely limited their application to the modelling of the large-scale ocean circulation. We describe a global circulation model that has, in principle, none of these limitations. The model utilizes the spectral element method that combines the geometrical flexibility of traditional finite element methods with the rapid converg...

Dynamics of the long-period tides

Abstract The long-period tides are a tool for understanding oceanic motions at low frequencies and large scales. Here we review observations and theory of the fortnightly, monthly and pole tide constitutents. Observations have been plagued by low signal-to-noise ratios and theory by the complex lateral geometry and great sensitivity to bottom slopes. A new spectral element model is used to compute the oceanic response to tidal forcing at 2-week and monthly periods. The general response is that of a heavily damped (Q ≈ 5) system with both the energy input from the moon and the dissipation strongly localized in space. The high dissipation result is probably generally applicable to all low frequency barotropic oceanic motions. Over much of the ocean, the response has both the character of a large-scale and a superposed Rossby wave-like character, thus vindicating two apparently conflicting earlier interpretations. To the extent that free waves are excited they are consistent with their being dominated by Rossby and topographic Rossby wave components, although gravity modes are also necessarily excited to some degree. In general, a modal representation is not very helpful. The most active regions are the Southern Ocean and the western and northern North Atlantic. These results are stable to changes in geometry, topography, and tide period. On a global average basis, the dynamical response of Mm is closer to equilibrium than is Mf.

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.

Multiscale Stochastic Preconditioners in Non-intrusive Spectral Projection

A preconditioning approach is developed that enables efficient polynomial chaos (PC) representations of uncertain dynamical systems. The approach is based on the definition of an appropriate multiscale stretching of the individual components of the dynamical system which, in particular, enables robust recovery of the unscaled transient dynamics. Efficient PC representations of the stochastic dynamics are then obtained through non-intrusive spectral projections of the stretched measures. Implementation of the present approach is illustrated through application to a chemical system with large uncertainties in the reaction rate constants. Computational experiments show that, despite the large stochastic variability of the stochastic solution, the resulting dynamics can be efficiently represented using sparse low-order PC expansions of the stochastic multiscale preconditioner and of stretched variables. The present experiences are finally used to motivate several strategies that promise to yield further advantages in spectral representations of stochastic dynamics.

Assessing the impact of observations on ocean forecasts and reanalyses: Part 2, Regional applications

The value of global (e.g. altimetry, satellite sea-surface temperature, Argo) and regional (e.g. radars, gliders, instrumented mammals, airborne profiles and biogeochemical) observation-types for monitoring the mesoscale ocean circulation and biogeochemistry is demonstrated using a suite of global and regional prediction systems and remotely-sensed data. A range of techniques is used to demonstrate the value of different observation-types to regional systems and the benefit of high-resolution and adaptive sampling for monitoring the mesoscale circulation. The techniques include Observing System Experiments, Observing System Simulation Experiments, adjoint sensitivities, representer matrix spectrum, observation footprints and spectral analysis. It is shown that local errors in global and basin-scale systems can be significantly reduced when assimilating observations from regional observing systems.

DDDAS approaches to wildland fire modeling and contaminant tracking

We report on two ongoing efforts to build dynamic data driven application systems (DDDAS) for (1) short-range forecasting of weather and wildfire behavior from real time weather data, images, and sensor streams, and (2) contaminant identification and tracking in water bodies. Both systems change their forecasts as new data is received. We use one long term running simulation that self corrects using out of order, imperfect sensor data. The DDDAS versions replace codes that were previously run using data only in initial conditions. DDDAS entails the ability to dynamically incorporate additional data into an executing application, and in reverse, the ability of an application to dynamically steer the measurement process

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...

Mantle 3He distribution and deep circulation in the Indian Ocean

[1] The World Ocean Circulation Experiment Indian Ocean helium isotope data are mapped and features of intermediate and deep circulation are inferred and discussed. The 3He added to the deep Indian Ocean originates from (1) a strong source on the mid-ocean ridge at about 19°S/65°E, (2) a source located in the Gulf of Aden in the northwestern Indian Ocean, (3) sources located in the convergent margins in the northeastern Indian Ocean, and (4) water imported from the Indonesian Seas. The main circulation features inferred from the 3 He distribution include (1) deep (2000-3000 m) eastward flow in the central Indian Ocean, which overflows into the West Australian Basin through saddles in the Ninetyeast Ridge, (2) a deep (2000-3000 m) southwestward flow in the western Indian Ocean, and (3) influx of Banda Sea Intermediate Waters associated with the deep core (1000-1500 m) of the through flow from the Pacific Ocean. The large-scale 3 He distribution is consonant with the known pathways of deep and bottom water circulation in the Indian Ocean.