Mathematical techniques are presented for modeling electromagnetic pro
pagation over an irregular boundary. The techniques are aimed at upgra
ding the Applied Physics Laboratory's Tropospheric Electromagnetic Par
abolic Equation Routine (TEMPER) model for radar propagation over terr
ain. The physical domain with an irregular boundary is mapped to a rec
tangular domain, where a numerical solution can be generated by the sa
me approach used in TEMPER. This new method is applied to several mode
l terrain problems and shown to be accurate and practical for a reason
able range of surface slopes. Interesting results are discussed for th
e shadowing of radar by terrain obstacles and the detection of low-fly
ing targets over mountainous terrain.