Hi Pamenifor
This is a classic example of a need to combine several structure types, as the culvert you describe is in reality kind of a composite structure where you have a closed pipe combined with an overtopping level (red line in your drawing).
The way to schematize this in your MIKE 11 model is simply to keep the definition of a culvert as you have made it already, and then you should insert an overflow weir structure in the model as well.
You will need to define a weir at the exact same location (identical chainage) as the culvert and with the geometry as defined by your 'red line'.
During simulation, MIKE 11 will then combine these two structures into a combined, composite structure and the total flow calculated at that location will be a sum of the flow that can go through the culvert pipe and the flow that eventaully passes over the overflow weir.
Regards
Torben