Two classes of variability in stratospheric trace species: (1) dynamically introduced tracer irregularities and (2) diurnal variations in photochemically active species, are investigated with regard to asynoptic satellite measurements. The fidelity with which the continuous synoptic behavior may be derived from discrete asynoptic measurements is explored. For both classes of variability several diagnostics of the continuous behavior (e.g., space-time spectra, synoptic maps, time-mean fields) are constructed from asynoptic measurements and compared with the true variability. Irregular tracer behavior of dynamical origin, as may follow large amplitude wave events or stratospheric warmings, is treated in a stochastic framework. An advected space-time process is constructed according to prescribed correlation scales, reflecting the spatial extent and lifetime of tracer anomalies which are introduced randomly into the field and advected about the globe in a specified zonal flow. In the case of diurnal variations, e.g., in photochemically active gases in the upper stratosphere and mesosphere, a solar waveform is prescribed to propagate through a latitudinal envelope. The structure of this solar signature is truncated to the sunlit side of the globe to mimic the response of photochemically active species. For both classes of variability (under plausible scales and advection speeds in the case of random tracer fluctuations) the continuous synoptic behavior is corrupted by aliasing from variance unresolved by asynoptic sampling. While some of this contamination may be eliminated by correctly assimilating combined (ascending plus descending) data, the behavior interpolated to synoptic times can be pathological. For random tracer variability the time-mean field, at least, can be correctly retrieved even if the behavior is undersampled, owing to cancellation of aliases in the averaging process. However, time-mean distributions of photochemically active species may not be faithfully captured, because diurnal fluctuations alias to the time-mean, and this aliasing is not eliminated by averaging over time. With the availability of contemporaneous measurements from several instruments viewing different regions of the globe (e.g., the Upper Atmosphere Research Satellite (UARS)), it may be possible to alleviate these difficulties, rooted in sampling deficiencies, by capitalizing on the extended information content of the combined data. The success of such a procedure will hinge on explicitly accounting for sampling irregularities inherent to the collective data ensemble.