I looked at your first ref concerning Seville, and discovered this in Wikipedia about the Tagarete:

A partir de 1849 se realizaron en la ciudad diversas obras que primero intubaron su cauce y posteriormente lo desviaron hacia el arroyo Tamarguillo con objeto de alejarlo del casco urbano, pues su existencia causaba inundaciones y era fuente de enfermedades sobre todo en verano cuando las aguas se estancaban.
http://es.wikipedia.org/wiki/Tagarete

This explains that the watercourse was put into pipes.

Culverted watercourses are surface watercourses that have been piped, usually under highways, driveways or housing developments. They are usually small in length, connecting at either end to an open watercourse.
http://www.chichester.gov.uk/index.cfm?articleid=14235

Culverts over watercourses look like vaults/arches, which could be how the Spanish term originates.

Culverts of this nature are not usually very long, however, so maybe this is not the right term (because I don't know what length we're actually talking about here), but I'm pretty sure it means covering and piping the watercourse.

Here are some examples:

The Moselle flows through Tottenham towards the lea valley, where it once posed a serious flood risk to the local villagers. This continued up until 1836 when a section around Tottenham High Road was covered over. Further culverting of the river continued up until 1906. Even with a large portion of the river now underground, it continued to annually fill and flood the town. This continued until the 1960's, when during a large redevelopment of the town the old culvert was replaced and rebuilt.
http://www.silentuk.com/writeups/moselle.html

The city walls were allowed to fall into disrepair after the siege of Cork in 1690. Following the culverting of the river channel in the late eighteenth century, the Grand Parade began to develop as a commercial centre. Shops and stores were opened along what is now the eastern section of Bishop Lucey Park.
http://www.corkpastandpresent.ie/places/grandparade/bishoplu...

The Duke's plan was to develop quality accommodation in the form of a crescent to rival that at Bath. Whilst the original site chosen proved to be unobtainable,the building was begun in 1780 on a site defined by a bend in the River Wye laid out as ornamental gardens.
The site required the culverting of the river, the stifling of at least one of the springs and possibly the destruction of at least part of the Roman baths. Considerable infill on one side was needed and piling into wet ground on the other, as well as the destruction of the gardens.
http://www.buxtongroup.co.uk/crescent_history.html

It is not a formal space but an accidental one created by the culverting of the River Frome in 1892 and has never managed to create a convincing urbanity.
http://www.jonestheplanner.co.uk/2013/07/bristol-fashion.htm...