Recent studies of ground-to-space beam propagation have revealed significant departures from Rytov theory when the beam diameter w0 is on the order of the atmospheric coherence width r0 . It has been shown that such departures from Rytov theory are primarily a consequence of beam wander and other low-order aberrations. In this paper we discuss modeling of the probability density function (PDF) for uplink beams. In particular, we show how the PDF transitions from lognormal statistics when w0 /r0 << 1 to the negative exponential distribution when w0/r0 >> 1. The most interesting regime is the transition region near w0/r0 = 1, where the statistical behavior of tracked and untracked beams differs significantly.© (2006) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.