The delta S (delta R)-2 question: The pulse-length dependence of signal power for Fresnel scatter

It is proposed that the enhanced echoes from the atmosphere observed with a vertically pointing radar are due to reflections from horizontally stratified layers. The general case in which there are many closely spaced layers at random heights is called Fresnel scatter. The variation of received power with transmitter pulse length is examined for various models of Fresnel backscatter. It is shown that for the model most often used in previous work, the power is proportional to the pulse length, and not to the pulse length squared. However, for more general models a more complex pulse length dependence is found.