Let me ask this...
Does the water over flow the dam when this happens (or elsewhere for that matter)? OR jsut back up?
I ask ,becuase, if it does flow out you can get an idea of the amount of water flow you would need to accomodate. This is a bare rule of thumb for laymen estimates only. The actual watershed estimates should be made so that an expert can reccomend the proper size taking into consideration the run off, legth of drain pipe, and slope.
For example, my pond has over taken the emergency overflow a time or two prior to it's renovation. It had an 18 or 20 inch diameter pipe and too much watershed. I witnessed the over flow once and the span of water was 20 feet wide and about 4 inches deep. That's over 6 square feet of cross sectional water (plus the flooded existing pipe. That would have translated to an additional 36" diameter overflow pipe at a minimum to of handled that event.
I say "at a minimum" because the slope of the pipe and the length play a role in the pipe size as well. The more flat the slope and the longer it is means you need a larger diameter pipe.
It looks like you have a long way to go to the ditch and pretty flat ground. If your pond is merely backing up and not overflowing the dam, an expert should be consulted to evaluate what I mentioned earlier.
