* Rains over Amazon, Australia, sucked water from seas
* Underlying rate of sea level rise continues - French study
By Alister Doyle, Environment Correspondent
OSLO, March 23 (Reuters) - Heavy rains from the Amazon to Australia have curbed sea level rise so far this century by shifting water from the oceans to land, according to a study that rejects theories that the slowdown is tied to a pause in global warming.
Sea level rise has been one of the clearest signs of climate change - water expands as it warms and parts of Greenland and Antarctica are thawing, along with glaciers from the Himalayas to the Alps.
But in a puzzle to climate scientists, the rate slowed to 2.4 millimetres (0.09 inch) a year from 2003 to 2011 from 3.4 mm from 1994-2002, heartening sceptics who doubt that deep cuts are needed in mankind's rising greenhouse gas emissions.
Writing in the journal Nature Climate Change on Sunday, experts said the rate from 2003-2011 would have been 3.3 mm a year when excluding natural shifts led by an unusually high number of La Nina weather events that cool the surface of the Pacific Ocean and cause more rain over land.
"There is no slowing in the rate of sea level rise" after accounting for the natural variations, lead author Anny Cazenave of the Laboratory for Studies in Geophysics and Spatial Oceanography in Toulouse, France, told Reuters.
In La Nina years, more rain fell away from oceans, including over the Amazon, the Congo basin and Australia, she said. It is unclear if climate change itself affects the frequency of La Ninas.
Rainfall over land only temporarily brakes sea level rise.
"Eventually water that falls as rain on land comes back into the sea," said Anders Levermann, a professor at the Potsdam Institute for Climate Impact Research, who was not involved in the study. "Some of it goes into ground water but most of it will drain into rivers, or evaporate."
HIATUS IN WARMING
The apparent slowing of sea level rise coincided with what the U.N. panel of climate experts calls a hiatus in global warming at the Earth's surface, when temperatures have risen less sharply despite record emissions of greenhouse gases.
"The slowdown in sea level rise ... is due to natural variability in the climate and is not indicative of a slowdown in the effects of global warming," Nature Climate Change said.
Many scientists suspect that the "missing heat" from a build-up greenhouse gases in the atmosphere is going into the deep oceans as part of natural variations in the climate.
But, because water expands as it warms, that theory had been hard to reconcile with the apparent slowdown in sea level rise.
Sea levels have risen almost 20 cms since 1900. The U.N. panel of climate experts expects an acceleration, with gains of between 26 and 82 cms over 100 years to the late 21st century.
Melting an ice cube with sides 7 kms (4.3 miles) long is roughly the equivalent of adding a millimetre of water to the world's oceans.
Last year, another study said that unusually heavy downpours over Australia in 2010 and 2011 had curbed sea level rise, before a rebound reaching a rate of about 1 centimetre a year globally, partly as water flowed back into the sea.
"It has tailed off in the past 12 months or so" to above 3 mm a year, said John Fasullo of the U.S. National Center for Atmospheric Research who was lead author of the Australia study.
For the Nature Climate Change study: http://dx.doi.org/10.1038/nclimate2159
(Reporting By Alister Doyle; Editing by Rosalind Russell)