The weakly nonlinear theory for internal solitary waves is reviewed an
d theoretical results of the vertical and horizontal structure of temp
erature, vertical displacements, and vertical and horizontal perturbat
ions to the wind field associated with steadily propagating solitary w
aves are presented in two idealized atmospheric configurations. One co
nfiguration is representative of solitary waves observed in the lower
troposphere and the other of solitary waves that occupy the entire tro
posphere. The important results of the theory are presented in a form
that can be readily used by observationalists. The results obtained ar
e then analyzed using actual rawinsonde data for two well-documented o
bservations of atmospheric solitary waves, which are analogous to the
two idealized configurations. The importance and difficulties of prope
rly identifying the waveguide within which the solitary wave is confin
ed are discussed. The fundamental role of a critical level in ducting
the disturbances and thus in defining the thickness of the waveguide i
s illustrated in the example dealing with the solitary wave occupying
the entire troposphere. Together, these two examples illustrate the de
cisions and compromises that must be made in applying the theory to th
e real atmosphere.