The single-scatter first Born approximation has previously been used to describe sonic boom scattering from spherically shaped turbules. Boulanger et al. [J. Acoust. Soc. Am. 98, 3412--3417 (1995)] used it to model the turbulent atmosphere (assuming isotropic turbulence) with reasonable success. An adaptation of this method to calculate the scattered wave from an ellipsoidally shaped turbule, using a Cartesian coordinate system centered at the turbule, gives more realistic results than those obtained from a spherical scatterer. The ellipsoidal method produces directionally dependent rise times, allowing better description of turbulence with mean wind flow, or anisotropic turbulence. This new approximation was applied to simulated booms from a T-38 flying at an altitude of 10 000 m, with a collection of turbules located in the planetary boundary layer (PBL). The size distribution and number of turbules used to simulate the atmosphere in the PBL were calculated using recorded meteorological data and Monte Carlo routines. This method of simulating the turbulent atmosphere has produced rise time distributions in good agreement with data empirically obtained from the Joint Acoustic Propagation Experiments performed at White Sands in 1991.