the correct use is profunda because 'agua' is feminine. There is a Spanish grammar rule which states that if the noun starts with an 'a' and where the stress is on that 'a', the definite article 'el' is used. http://spanish.about.com/od/adjectives/a/el_for_la.htm As with anything there always exceptions.
Um, gernt I don't know how to tell you this, but those examples on google that you refer to are either non-natives getting confused by the apparent masculinity of el agua (my favorite is "AGUA PROFUNDO, LP is a Texas Domestic Limited Partnership"), or the profundo is the adjective of something other than water.
un pozo de agua profundo : "a deep water well"
un flujo de agua profundo : "a deep water flow"
un charco de agua profundo : "a deep water puddle"
Agua is decidedly feminine, as indicated by the plural las aguas.
I wrote el agua, and the DL correction changed the article to la and said that "agua" is masculine. But that's not correct, as I understand it--agua is a feminine noun preceded by el because la agua does not come trippingly off the tongue. Must be a programming issue with DL though--when it corrects articles, it must assume word is the gender of the corrected article??
Duolingo is just a computer :-) And it is true that there are errors in the data. Maybe when an answer doesn't match the list, the page could be softened a bit so that it sounds less like a teacher marking you wrong. (Anyone can volunteer to contribute to a course at the bottom of the same page where you add a language course).