How many calories does rowing expend when done rigorously?

Are you referring to on the water rowing, or rowing indoors on an ergometer? Both burn calories at a very rapid rate.

On a concept 2 erg machine, you can select a screen that displays the number of calories per hour.

On the water, it is a bit harder to gauge, but if you plan on rowing competitively, you can easily burn over 1000 calories in a 2-3 hour session.

From my experience as a varsity collegiate rower, throughout our rigorous two-a-day practice sessions, it is necessary to consume nearly 5000 calories a day, and weight can still be lost.

Depending on the level you seek to row at, you can easily burn a huge amount of calories.