Abstract: Many of the atmospheric phenomena with the greatest potential impact in future warmer climates are inherently multiscale. Such meteorological systems include hurricanes and tropical cyclones, atmospheric rivers, and other types of hydrometeorological extremes. These phenomena are challenging to simulate in conventional climate models due to the relatively coarse uniform model resolutions relative to the native nonhydrostatic scales of the phenomonological dynamics. To enable studies of these systems with sufficient local resolution for the multiscale dynamics yet with sufficient speed for climate-change studies, we have developed a nonhydrostatic adaptive mesh dynamical core climate studies. In this talk, we present an adaptive, conservative finite volume approach for moist non-hydrostatic atmospheric dynamics. The approach is based on the compressible Euler equations on 3D thin spherical shells, where the radial direction is treated implicitly to eliminate time step constraints from vertical acoustic waves. The spatial discretization is the equiangular cubed-sphere mapping, with a fourth-order accurate discretization to compute flux averages on faces. By using both space-and time-adaptive mesh refinement, the solver allocates computational effort only where greater accuracy is needed. The main focus are demonstrations of the performance of this AMR dycore on idealized problems directly pertinent to atmospheric fluid dynamics. We start with test simulations of the shallow water equations on a sphere. We show that the accuracy of the AMR solutions is comparable to that of conventional, quasi-form mesh solutions at high resolution, yet the AMR solutions are attained with 10 to 100x fewer operations and hence much greater speed. The remainder of the talk concerns the performance of the dycore on a series of tests of increasing complexity from the Dynamical Core Model Intercomparison Project, including tests without and with idealized moist physics to emulate hydrological processes. The tests demonstrate that AMR dynamics is a viable and highly economical alternative for attaining the ultra-high resolutions required to reproduce atmospheric extreme phenomena with sufficient accuracy and fidelity.

Abstract: A strict throughput requirement has placed a cap on the degree to which we can depend on the execution of single, long, fine spatial grid simulations to explore global atmospheric climate behavior in more detail. Running an ensemble of short simulations is economical as compared to traditional long simulations for the same number of simulated years, making it useful for tests of climate reproducibility with non-bit for bit changes. We test the null hypothesis that the climate statistics of a full-complexity atmospheric model derived from an ensemble of independent short simulation is equivalent to that from a long simulation. The climate statistics of short simulation ensembles are statistically distinguishable from that of a long simulation in terms of the distribution of global annual means, largely due to the presence of low-frequency atmospheric intrinsic variability in the long simulation. We also find that model climate statistics of the simulation ensemble are sensitive to the choice of compiler optimizations. While some answer-changing optimization choices do not effect the climate state in terms of mean, variability and extremes, aggressive optimizations can result in significantly different climate states.

Abstract: A problem of quasi-static growth of an arbitrary shaped-crack along an interface requires many times of iterations not only for find a spatial distribution of discontinuity but also for determining the crack tip. This is crucial when refining model resolution and also when the phenomena progresses quickly from one step to another. We propose a mathematical reformulation of the problem as a nonlinear equation and adopt different numerical methods to solve it efficiently. Compared to a previous work of the authors, the resulting code shows a great improvement of performance. This gain is important for further application of aseismic slip process along the fault interface, in the context of plate convergence as well as the reactivation of fault systems in reservoirs.

Abstract: In 1974 Lawson and Hanson produced a seminal active set strategy to solve least-squares problems with non-negativity constraints that remains popular today. In this paper we present TNT-NN, a new active set method for solving non-negative least squares (NNLS) problems. TNT-NN uses a different strategy not only for the construction of the active set but also for the solution of the unconstrained least squares sub-problem. This results in dramatically improved performance over traditional active set NNLS solvers, including the Lawson and Hanson NNLS algorithm and the Fast NNLS (FNNLS) algorithm, allowing for computational investigations of new types of scientific and engineering problems. For the small systems tested (5000x5000 or smaller), it is shown that TNT-NN is up to 95x faster than FNNLS. Recent studies in rock magnetism have revealed a need for fast NNLS algorithms to address large problems (on the order of 10^5 x 10^5 or larger). We apply the TNT-NN algorithm to a representative rock magnetism inversion problem where it is 60x faster than FNNLS. We also show that TNT-NN is capable of solving large (45000x45000) problems more than 150x faster than FNNLS. These large test problems were previously considered to be unsolvable, due to the excessive execution time required by traditional methods.