Rotating stall is a phenomenon in axial compressors in which regions of separated, axially reversed flow propagate circumferentially in the direction of rotor rotation. These rotating regions of separated flow are associated with high amplitude pressure fluctuations. These pressure fluctuations force vibrations and can propagate downstream. The front stages of multi-spool axial compressors operate in rotating stall for off-design, but normal operation. Because rotating stall is experienced in normal operation, minimizing the structural fatigue and compressor operability impacts are better achieved by characterizing the rotating stall state rather than attempting to eliminate it. For many compressors, the spatial and temporal scales of rotating stall are accurately described by a simple, harmonic description. For others, the pressure field is spatially and temporally more complicated.The observation of these spatially and temporally complicated pressure fluctuations in front stage axial compressors motivate the following research questions: What are the spatial and temporal scales of the complicated rotating stall pressure fields? Are these fields structured? Can these fields be characterized with simple metrics? Can these fields be described by a simple harmonic equation with stochastic variation? If so, what is the magnitude of the variation?This dissertation used unsteady static pressure measurements at multiple locations on the rotor casing to observe rotating stall cells that are intermittent. The cells stochastically originate and terminate and their duration is less than the full annulus. Spatial modes of a quasi-instantaneous blade pressure distribution were measured and decomposed. This decomposition showed a variation in blade pressure distribution shape and amplitude. The correlation length scale and the convergence timescale are introduced as metrics which characterize the complicated pressure fields as the operating point is changed. For some operating points, the convergence timescale exceeds 150 rotor revolutions. Stochastic variation is introduced to different mathematical models which match the statistical properties of these complicated pressure fields. This reveals that very small variations ($<$ 0.1 percent) in the phase and rotating speed of a simple harmonic rotating stall state can lead to the spatially and temporally complicated pressure fields that were experimentally observed.