HR: 0800h
AN: NG31A-0850    [Abstracts]
TI: Time-step sensitivity of nonlinear atmospheric models: numerical convergence, truncation error growth and ensemble design
AU: * Teixeira, J
EM: teixeira@nrlmry.navy.mil
AF: Naval Research Laboratory, 7 Grace Hopper Ave, Monterey, CA 93943 United States
AU: Reynolds, C
EM: reynolds@nrlmry.navy.mil
AF: Naval Research Laboratory, 7 Grace Hopper Ave, Monterey, CA 93943 United States
AU: Judd, K
EM: judd@nrlmry.navy.mil
AF: Naval Research Laboratory, 7 Grace Hopper Ave, Monterey, CA 93943 United States
AB: Computational models based on discrete dynamical equations are a successful way of approaching the problem of predicting or forecasting the future evolution of dynamical systems. For linear and mildly non-linear models, the solutions of the numerical algorithms in which they are based, converge to the analytic solutions of the underlying differential equations, for small time-steps and grid-sizes. In this paper, we investigate the time-step sensitivity of three non-linear atmospheric models of different levels of complexity: the Lorenz equations, a quasi-geostrophic (QG) model and a global weather prediction system (NOGAPS). We show that for chaotic systems, numerical convergence cannot be guaranteed forever. The decoupling of solutions for different time-steps follows a logarithmic rule similar for the three models. In regimes that are not fully chaotic, the Lorenz equations are used to show that different time-steps may lead to different model climates and even different regimes. We propose a simple model of truncation error growth in chaotic systems that reproduces the behavior of the QG model error growth for different time-steps. Experiments with NOGAPS suggest that truncation error is a substantial component of total forecast error of the model. Ensemble simulations with NOGAPS show that using different time-steps is a simple and natural way of introducing an important component of model error in ensemble design.
DE: 3337 Numerical modeling and data assimilation
DE: 3210 Modeling
DE: 3220 Nonlinear dynamics
DE: 3230 Numerical solutions
DE: 3240 Chaos
SC: Nonlinear Geophysics [NG]
MN: 2004 AGU Fall Meeting