1. In synoptic meteorology, a detailed study of the state of the atmosphere based on observations, usually including a separation of the entity into its component patterns and involving the drawing of families of isopleths for various elements. Thus, the analysis of synoptic charts may consist, for example, of the drawing and the interpretation of the patterns of wind, pressure, pressure change, temperature, humidity, clouds, and hydrometeors, all based on observations taken or forecast simultaneously. 2. A procedure to project the state of the atmosphere (or any system) as known from a finite set of imperfect, irregularly distributed observations onto a regular grid or to represent the atmospheric state by the amplitude of standard mathematical functions. The grid and/or functional expansion allows for subsequent forecasts by numerical integration or for easy diagnostic study. An analysis may be looked upon as a space–time interpolation system. Essential ingredients of analysis are a background field, usually a short-range forecast although persistence and climatology are options, a forecast model, knowledge of the relative error of the many different observational platforms employed as well as knowledge of the error in the background field, and the spatial covariance of the various errors. Real time computational considerations generally limit the complexity of methods used. Historically important is the subjective hand analysis, that is, drawing isobars on a map given mean sea level pressure at a set of observing stations. Most analysis systems in the past have been at best 3D spatial analyses; time–space analysis systems have recently emerged at operational prediction centers. A long series of analyses is of great utility for studying the behavior of the atmospheric climate system. See reanalysis, variational objective analysis.