Accelerating applications algorithmically
In this simulation, (a) shows the initial position of a tracer field (a cosine-bell with a maximum value of 1,000 units). After transporting this field one complete revolution, it returns to its initial position. Discrepancies with the initial values are the numerical errors in the algorithm. The semi-Lagrangian multi-tracer transport algorithm is used for the simulations and a cubed-sphere grid is used for the discretization. Note that the transport purposely traverses the "corners" and "edges" of this grid to make the test more stringent. Part (b) shows the error of the numerical solution as a function of different grid resolutions (Nc) and time steps (delta t). Part (c) is the numerical solution after one complete revolution without constraints on the positivity yielding an non-physical solution. And (d) shows an improved solution with monotonic filtering that avoids spurious undershoots.A new numerical approach for simulating the simultaneous motion of multiple constituents in the atmosphere as they are transported by the atmospheric flow is a highlight from FY2009. These quantities can be basic physical components of the atmosphere such as water vapor, or they can be specific human-related compounds such as the fine particles released from forest clearing or from urban pollution. This basic problem of determining the path of a substance, or tracer, as it is transported by atmospheric flow is surprisingly difficult because one needs to conserve the quantities being translated while keeping concentrations nonnegative. Its practical significance in modeling is that it allows researchers to attribute the concentrations of tracers at a given location and a given time to their original sources.
In an operational climate model such as the CCSM, transport algorithms (also known as advection algorithms) are responsible for tracking several physical variables and hundreds of chemical constituents. Because of the enormous number of these variables, simulating the transport of these quantities individually is computationally intensive. An efficient strategy that avoids separate advection for each tracer is to use the so-called multi-tracer algorithms optimized for simultaneous transport of a large number of constituents. Technically, a conservative, semi-Lagrangian approach known as incremental remapping lends itself to a mathematical augmentation that enables reusing the elements of trajectory evaluation and flux reconstruction common to the transport of all tracers. Thus the entire multi-tracer advection can be made extremely efficient and is a new approach to this problem. This transport scheme based on the conservative semi-Lagrangian method has been developed for cubed-sphere geometry to become part of the Community Atmosphere Model (CAM). Distinctive features of this approach are its multidimensionality and compactness that facilitate distributing the computations among large numbers of processors.
In FY2010, the new multi-tracer algorithm will be tested in the HOMME/CAM framework. This involves efficient parallel implementation of the algorithm in HOMME and long-term integration with CAM physics. This will facilitate a thorough testing of the algorithm with dozens of different chemical fields before it is ported to the operational CCSM framework.
This work advances CISL's science frontier in algorithmic acceleration by developing new algorithms and computational approaches to produce simulations capable of addressing grand challenges. Specifically, it fulfills a strategic action item to accelerate applications algorithmically by developing new numerical methods, AMR, new solvers, and new time integration schemes. This work is supported by NSF Core funding.