Mechanisms for the Development of Locally Low Dimensional Atmospheric Dynamics

Michael Oczkowski

Dept. of Meteorology
University of Maryland at College Park

The complexity of atmospheric instabilities is investigated by numerical experiments and diagnostic tools that do not require the assumption of linear error dynamics. These tools include the well established analysis of the local energetics of the atmospheric flow and the recently introduced Ensemble-dimension (E-dimension). The E-dimension is a local measure that varies in both space and time. It quantifies the distribution of the variance of an ensemble of solutions in phase space over a geographically localized region. The E-dimension is maximal, i.e., equal to the number of ensemble members k, when the variance is equally distributed between k phase space directions. The more unevenly distributed the variance, the lower the E-dimension is.

Regions of locally low dimensional chaos in the atmospheric dynamics can be identified by drawing maps of the E-dimension and locating the low E-dimensional regions. Numerical experiments with the standard 2-layer quasi-geostrophic (QG) model and the state-of-the-art operational Global Forecast System of the National Centers for Environmental Prediction (NCEP GFS) at a reduced resolution are carried out to identify processes that can lead to locally low dimensional behavior. The experiments with the 2-layer QG model reveal a new aspect of the role leading edge dynamics plays in the development of local baroclinic instabilities: the leading edge of the eastward propagating wave packet is not only the region of the fastest local perturbation growth, but also a region where low dimensional chaotic behavior is likely to occur. Furthermore, the results with the NCEP GFS show a surprisingly wide range of dynamical processes can lead to low dimensional behavior. The processes identified in this paper are combinations of local baroclinic and barotropic instabilities, downstream development of upper tropospheric wave packets, phase-shifts of finite amplitude waves, and anticyclonic wave breaking. Further processes that can lead to low dimensional behavior are expected to exist.

The practical implication of the above findings is that a wide range of synoptic scale weather events exist whose prediction can be significantly improved by enhancing the initial conditions of numerical weather forecasts. The potential for such forecast improvements is demonstrated by studying the forecast impact of a targeted weather observations mission from the 2000 Winter Storm Reconnaissance (WSR2000) program.