Research Topics

Uncertainty Quantification

Atmospheric and Oceanic General Circulation Models rely on a large number of inputs (such as initial and boundary conditions, forcing fields, subgrid scale model parameters) to forecast the atmospheric and oceanic states. In most cases this input data is known only approximately, and as such model forecasts are uncertain. To be useful, oceanic and atmospheric models must include reliable estimates of the uncertainty in their outputs. The broad goal of Uncertainty Quantification (UQ) is to investigate input and output model uncertainties. More specifically, UQ has 5 inter-related objectives that can be described as: Uncertainty Identification, Uncertainty Characterization, Uncertainty Propagation, Uncertainty Analysis and Uncertainty Reduction. One approach to UQ is the so-called Polynomial Chaos Expansions. Dr. Iskandarani has partnered with Dr. A. Srinivasan, Dr. W.C. Thacker, and Dr. O.M. Knio to explore the applicability of PCEs in oceanic simulations. To date PCEs have been used to study uncertainty in the Gulf of Mexico circulation due to nesting boundary conditions, to investigate parametric uncertainties in HYCOM's mixed-layer model and air-sea interactions coefficients, and to assess uncertainties in an oil spill model.
Uncertainty in Nesting Boundary Conditions

Uncertainty in Loop Current position from 49-member HYCOM ensemble where nesting conditions on the southern boundary are perturbed. The figure shows the 17 cm sea surface height contour, a proxy for the Loop Current, from each realization in a different color. The middle and right figures show the mean and standard deviation of SSH from the Polynomial Chaos Expansions.
Parametric Uncertainty Studies

Parametric uncertainy in KPP parameters and air-sea interaction coefficients. Left panel: the expected Sea Surface Temperature and the spatially averaged expected SST within the hurricane track box; Ivan's center is marked with a red dot on the track. Middle panel: time evolution of the area-averaged expected SST in the control box with one standard deviation bounds. Right panel: time evolution of the SST variance, in fraction, contributed by the Richardson number (red), background viscosity (green), background diffusion (blue) and drag coefficient (black) uncertainty. The uncertainty in the drag coefficient dominates the other when the hurricane approaches.
[1] Alexanderian, Justin Winokur, Ihab Sraj, Mohamed Iskandarani, Ashwanth Srinivasan, William C. Thacker, and Omar M. Knio. Global sensitivity analysis in an ocean general circulation model: a sparse spectral projection approach. Computational Geosciences, 2012. [ DOI | Abstract ]
[2] William C. Thacker, Ashwanth Srinivasan, Mohamed Iskandarani, Omar M. Knio, and Mathieu Le Henaff. Propagating boundary uncertainties using polynomial expansions. Ocean Modelling, 43-44:52-63, 2012. [ DOI | http | Abstract ]

Model Development

Ocean model development is critical to keep pace with the increasing demands for more detailed simulation of various ocean phenomena. We have been engaged in a number of efforts to either enhance existing Ocean General Circulation models or develop new ones. Below is a short description of these efforts.
Lagrangian Oil Model
Spectral Element Ocean Model
Spectral element offer an attractive alternative to finite-difference and finite-volume based codes when geometric flexibility and high-order accuracy are at a premium. The primary advantages of the methods are: the ability to use unstructured grids, rapid convergence to the solution, vanishing levels of spurious numerical dissipation and dispersion, scalable parallel computations. Multiple versions of a spectral element code exist for either a one layer shallow water model, a three-dimensional hydrostatic code, and a 2D incompressible flow solver.
Gravity Current Simulations
Gravity current mixing using a non-hydrostatic spectral element model at Reynolds number of 100,000 but free-slip boundary condition on all walls. Clicking on the picture will show an animation of the gravity current.




Vortex interaction in incompressible flows
Investigating seconday eye wall replacement by 2D vortex dynamics. Clicking on the picture will show an animation of the interacting vortices.
Yumin Moon, David S. Nolan, and Mohamed Iskandarani. On the use of two-dimensional incompressible flow to study secondary eyewall formation in tropical cyclones source: Volume: 67 issue: 12 pages: Published: 2010. Journal of the Atmospheric Sciences, 67:3765-3773, 2010. [ DOI | Abstract ]
Abyssal flow in Indian Basin
Inverted 1.5 layer model of the flow in the Abyssal Central Indian Basin using the shallow water model.

High Performance Computing

Most geophysical fluid flow problems are CPU-bounds given the vastness of the enclosing domains and the multiscale nature of their flows. Optimizing models to run on state of the arts computing hardware is one way to expand the range of problems that can be practically solved. The problem is compounded by the requirements of uncertainty quantifications where ensemble runs must be processed within a reasonable amount of time to assess the uncertainty in a given forecast. Parallel computing is one way to leverage the power of multiple processor to speed up computational time. The spectral element code has been parallelized using the now traditional approach of SPMD programming on distributed memory processors using message-passing; an enduring question is on implementing efficient multi-level parallel solvers. More recently we have begun to explore the use of Graphical Processing Units to speed up the calculations in the Lagrangian oil model.