If you use the basic Vf + Rs model, there is a linear power term (from Vf) and a quadratic term (from Rs). That is, power dissipated is: Vf * I + Rs * I^2.

For a waveform, the power from Vf comes from average current, while that from Rs comes from RMS current.

So it's definitely more than average, but not quite RMS, and certainly not peak.

It gets more complicated if you include a more nuanced model of Vf (a power series, or the exponential proper), and temperature dependence. (Note that, as the diode is allowed to heat up, it becomes more efficient in the forward direction! And also less efficient in reverse -- watch out for that leakage at high temperatures.) You'd be better off SPICEing that, though.

Why power? Until extremely high currents (above the surge rating), the limiting factor is heat. So the diode rating also depends on the heatsinking: a B340 with minimal pads is good for about as much as a (frame-lead) SOD-123F with a smaller die, but more heatsinking. (PMEGxxxx parts come to mind.)

Small dies are also better for high frequency operation. This isn't a problem at your frequencies, though.

Tim