Greg Hakim, University of Washington
The concepts of balance and imbalance have been closely related to state estimation since the advent of numerical weather prediction. Early NWP practitioners recognized the need for truncated (balance) models due to limited computational resources and the projection of initial conditions onto fast motions not associated with weather disturbances. Balance, slow modes, and initialization have been closely linked over the years, with knowledge of balance exploited to improve state estimation and initialization. In this talk I will argue that we have reached a point of opportunity where state estimation no longer requires balance assumptions, and in fact, the state estimation process may now be exploited to define balance.
A key aspect of this new approach derives from the fact that the state is known only probabilistically, and observations of the system constrain the probability distributions through state estimation. Given these probabilistic estimates of the state, balance and imbalance can be defined through conditional probabilities, which may vary in space and time. For example, state-dependent inversion operators for Ertel potential vorticity may be determined statistically without specifying balance or boundary conditions. The range and null space of these statistical operators provide a convenient framework for defining the balanced and unbalanced part of the state, respectively. Such definitions are attractive because they hold for arbitrary departures from states of rest and for state variables that have unknown relationships to potential vorticity (e.g. cloud microphysical fields). Specific examples will be given using state samples drawn from an ensemble Kalman filter.