Present and emerging technologies for communication, remote sensing, object tracking and identification, nonintrusive inspection of materials, etc., place increasingly greater demands on wave data gathering, data interpretation, signal processing, and predictive modeling. While large-scale computing is inextricably coupled into this process, computing alone cannot address problems of classification and identification (data inversion) without a parametrized model. With the present toward wideband signals and higher frequencies, numerically large problems in various applications and disciplines (on the scale of relevant wavelength) are encountered where previously they were not when the bandwidth was limited and the frequency moderate. In this paper, it is argued that an effective parametrization of a complex propagation, interrogation, or identification channel between a source and a receiver should be structures most effectively around 'observables' in data. Such observables are prominent features like spikes, dips, periodicities, relatively smooth oscillations, etc. In an observable- based parametrization (OBP), one seeks to relate these features to various fundamental wave processes that are operative in the signal-environmental (target) interaction. Observables in data are generated by such wave processes and by interference between them as problem parameters (frequency, aspect, time) vary. At high frequencies, a propagation and/or scattering environment may have relatively extended regular portions (or relevant wavelength scales) interrupted by more localized (in terms of wavelengths) strong perturbations that connect with other relatively regular portions. In this way, one may decompose the environment into a regime of wavelength-dependent propagating regions and scattering or coupling regions, which are assembled into a self-consistent system. By OBP, one attempts to construct wave objects which are 'good propagators' in regular regions, i.e., they describe the physics of the relevant propagation mechanism as directly as possible. If the system is such as to cause multiple scattering of propagating (traveling) waves, then these multiple effects can often be expressed 'more physically' in terms of oscillatory (standing wave) events, either in a cross section of a layered configuration, in which they synthesize traveling guided modes in the layer or throughout a propagation volume, in which case they synthesize resonant modes. Because of the fundamentally distinct and complementary roles played by traveling and oscillatory wave events, these events, and their self-consistent hybrid combinations, are cornerstones for OBP.