Practical Predictability of Flows with Many Scales of Motion (Invited Presentation)

With advances in both observational and computational capabilities, data assimilation and prediction that treat a range of spatial or temporal scales simultaneously are increasingly feasible.  This raises the question of predictability in practice, for a given observing network, across that range of scales.  Basic insights follow from generalizing Lorenz’s (1969) model for the intrinsic predictability of isotropic, homogeneous turbulence to include data assimilation.  When the exponent of the flow’s kinetic-energy power law is -3 (the situation that characterizes atmospheric motions for scales larger than roughly 400 km), even scales smaller than the resolution of the observational network can be analyzed and predicted skillfully.  For an exponent of -5/3 (the situation that characterizes atmospheric scales below roughly 400 km), recovery of unobserved scales by the assimilation scheme is much more limited and skillful prediction is possible only for observed scales.