Predictability of the Stable Atmospheric Boundary Layer

Abstract

The partial differential equation set for the horizontally homogeneous nocturnal boundary layer under first-order closure is discretized and truncated to a two-layer system. This system can be treated as a coupled four-layer ordinary differential equation set Using techniques of nonlinear dynamics, including numerical continuation and nonlinear stability analysis, characteristics of the solutions are developed. The bifurcation diagrams show classic S-shaped behavior so that the equations support multivalued solutions for certain values of external parameters. Both stable and unstable solution regimes exist with multiple, stable limit points. The results have strong implications for the predictability of the stable boundary layer in that even slight changes in initial conditions (or perturbations) would lead to quite different solutions in terms of temperature and wind speed for the regions of multivalued solutions. Practically, this means that predictions of frost or pollution dispersion may not be made with confidence for certain parameter regimes. If this type of behavior holds in the full partial differential equation set, it also means that additional physics or numerical sophistication in models will not improve the prediction of winds or temperature.