Electromagnetic plane wave scattering by a partially filled trough on the ground has been analyzed by high frequency asymptotic techniques based on Geometrical Theory of Diffraction. Field in the trough region has been formulated in terms of parallel plane waveguide modes, whose excitation (coupling) coefficients are obtained by ray-mode conversion techniques. Previous investigation for obtaining such excitation coefficients has now been extended to account for multiple edge interaction effects. Numerical calculation has been done extensively and thus obtained results are then compared with those by other methods. Good agreements have been observed except for grazing incidence case. It is found that first and secondary modal re-radiation fields from the indented trough region play an important role for scattering far field, and primary edge diffracted field contributes mainly to reflection boundary direction. It is also found that the formulation with these higher order interaction terms can be used even for narrow aperture cases, as well as shallow cases.