In this paper the weak scatter scintillation theory is reformulated to show explicitly the ramifications of an arbitrarily large ionospheric outer scale. The measured temporal phase spectrum, for example, is effectively truncated at a fixed frequency corresponding to the detrend time or the length of the data interval over which it is measured (whichever is smaller). As a consequence, the rms phase exhibits a complicated dependence on the relative irregularity drift velocity and the propagation geometry. This effect has not been included in previous analyses. By comparison, intensity scintillation data are intrinsically high-pass filtered by the diffraction process. By taking advantage of this fact a simple closed form expression for the S4 intensity scintillation index has been derived. The theory is applied to representative data sets from the Wideband satellite. The interpretation of the ionospheric parameters deduced from the analysis is also discussed.