Consistent approximate models of the global atmosphere: shallow, deep, hydrostatic, quasi-hydrostatic and non-hydrostatic

We study global atmosphere models that are at least as accurate as the hydrostatic primitive equations (HPEs), reviewing known results and reporting some new ones. The HPEs make spherical geopotential and shallow atmosphere approximations in addition to the hydrostatic approximation. As is well known, a consistent application of the shallow atmosphere approximation requires omission of those Coriolis terms that vary as the cosine of latitude and of certain other terms in the components of the momentum equation. An approximate model is here regarded as consistent if it formally preserves conservation principles for axial angular momentum, energy and potential vorticity, and (following R. Müller) if its momentum component equations have Lagrange's form. Within these criteria, four consistent approximate global models, including the HPEs themselves, are identified in a height-coordinate framework. The four models, each of which includes the spherical geopotential approximation, correspond to whether the shallow atmosphere and hydrostatic (or quasi-hydrostatic) approximations are individually made or not made. Restrictions on representing the spatial variation of apparent gravity occur. Solution methods and the situation in a pressure-coordinate framework are discussed. © Crown copyright 2005.

One’s own soundtrack: affective music synthesis

Computer music usually sounds mechanical; hence, if musicality and music expression of virtual actors could be enhanced according to the user’s mood, the quality of experience would be amplified. We present a solution that is based on improvisation using cognitive models, case based reasoning (CBR) and fuzzy values acting on close-to-affect-target musical notes as retrieved from CBR per context. It modifies music pieces according to the interpretation of the user’s emotive state as computed by the emotive input acquisition componential of the CALLAS framework. The CALLAS framework incorporates the Pleasure-Arousal-Dominance (PAD) model that reflects emotive state of the user and represents the criteria for the music affectivisation process. Using combinations of positive and negative states for affective dynamics, the octants of temperament space as specified by this model are stored as base reference emotive states in the case repository, each case including a configurable mapping of affectivisation parameters. Suitable previous cases are selected and retrieved by the CBR subsystem to compute solutions for new cases, affect values from which control the music synthesis process allowing for a level of interactivity that makes way for an interesting environment to experiment and learn about expression in music.