A solution of the inviscid rapid distortion equations of a stratied flow with homogeneous shear is proposed, extending the work of Hanazaki and Hunt (J. Fluid Mech., 2004,vol. 507, pp. 1-42) to the two horizontal velocity components. The analytical solution allowed the determination of the spectral tensor evolution at any given time starting from a known initial condition. By following the same approach adopted by Mann (J.Fluid Mech., 1994, vol. 273, pp. 141-168), a model for the velocity spectral tensor in the atmospheric boundary layer is obtained where the spectral tensor, assumed to be isotropic at the initial time, evolves until the break-up time where the spectral tensor is supposed to achieve its final state observed in the boundary layer. The model predictions are compared with atmospheric measurements obtained over a forested area, giving the opportunity to calibrate the model parameters and further validation is provided by lowroughness data. Characteristic values of the model coffecients and their dependence on the Richardson number are proposed and discussed.