Over the past two decades there have been numerous articles in the literature discussing methods of obtaining global-scale synoptic mathematical representations from asynoptic satellite observations. These studies cover a wide range of viewpoints, ranging from claims of presenting synoptic maps to opinions stating that synoptic representations cannot be obtained from asynoptic data alone, and that physical models are needed to augment the measurements. We review and comment on many of these previous studies. We do not believe that previous published representations generated from Upper Atmosphere Research Satellite data alone for variables that exhibit significant diurnal variations, are indeed synoptic. However, we show that UARS data can be used to estimate useful synoptic approximations without the need for physical models. Using a two-dimensional Fourier least squares algorithm, we calculate mathematical approximations to synoptic maps. We provide examples for ClO, ClONO2, NO2, O3, CH4, temperature, and winds and discuss how they can provide new information on both the chemistry and dynamics of the atmosphere. ¿ 2001 American Geophysical Union