"What we found is that some of the levee failures in New Orleans were places where subsidence was highest," said Dr Tim Dixon of the University of Miami Rosenstiel School of Marine and Atmospheric Science.

In some cases the ground had subsided a minimum of 3 feet (1 metre) which probably put the levees that were built more than 40 years ago lower than their design level.

"Now we have a good idea which parts of New Orleans are subsiding and at what rate. That is something that was not known before," said Dr Falk Amelung, a geologist and co-author of the report published in the journal Nature.

The researchers said they did not know what was causing the subsidence. One possibility was that the whole area is slowly sliding into the Gulf of Mexico. It could also be due to the drainage of shallow sediment. "It's probably a combination of both," Amelung said in an interview.

When he and his colleagues included global rises in sea level in the calculations the average rate of subsidence relative to sea level was an average 8 mm (0.3 inch) per year.

If the annual rate is multiplied over decades or even a century New Orleans will be lower than it is today, which the scientists said should be considered in reconstruction plans for the city.

"By 2106, for example, the ground will be nearly three feet lower on average," said Amelung.

The scientists developed the map by analysing the radar images and examining how structures in the city reflected the signal. Some of the areas hardest hit by the hurricane were built on drained marsh sediments.

Similar maps have been used to look at volcanic activity in Hawaii and tectonic activity in San Francisco.