One Saddle Point and Two Types of Sensitivities within the Lorenz 1963 and 1969 Models

The fact that both the Lorenz 1963 and 1969 models suggest finite predictability is well known. However, less known mechanisms (i.e., sensitivities) within models, which lead to predictability, are different. Additionally, mathematical physical relationship between these two has not been fully documented. New analyses, along with a literature review, performed here provide insights regarding similarities differences for models. represent different systems, one convection other barotropic vorticity. From perspective of complexities, (L63) model limited-scale nonlinear; (L69) closure-based, physically multiscale, mathematically linear, numerically ill-conditioned. former possesses sensitive dependence solutions on initial conditions, as butterfly effect, latter contains numerical sensitivities due an ill-conditioned matrix large condition number variance growth rates). Here, we illustrate existence saddle point at origin common feature produces instability in systems. Within chaotic regime L63 nonlinear model, unstable constrained by nonlinearity, dissipation, yielding time varying rates orbit, and, thus, (finite) conditions. L69 linear multiple modes various appear, specific mode most during interval) imposing saturation assumption, thereby system rate. Both were interchangeably applied qualitatively revealing nature weather climate. only single type examined linearly respectively), easily captures instability. Thus, estimate limit using either above or without additional assumptions (e.g., saturation), should be interpreted caution generalized upper atmospheric predictability.