SAO PAULO (Reuters) - Chinese investment in Brazil spiked in 2010 but has fallen since then, according to official data and independent studies, as executives grew frustrated with Brazil's slowing economy and protectionist policies.

Following are signs of how Chinese activity in Brazil has cooled in recent years:

* According to Brazilian government data, foreign direct investment (FDI) from China jumped from $83 million in 2009 to $395 million in 2010. Since then, though, FDI fell to $179 million in 2011, $185 million in 2012 and only $96 million in the first nine months of 2013.

However, official data only capture a fraction of the reality, since many Chinese companies invest in Brazil via subsidiaries based in the Caribbean or elsewhere.

A fuller study published in June by the China-Brazil Business Council (CBBC), a Rio de Janeiro-based group, included such ventures. It found that Chinese FDI in Brazil soared from $95 million in 2009 to a whopping $13.1 billion in 2010.

Since then, though, Chinese FDI in Brazil fell to $8 billion in 2011 and $2.8 billion in the first six months of 2012, the last period for which the CBBC tabulated such data.

* Total FDI from all nations in Brazil was fairly resilient until dropping off in recent months, according to government data. Overall FDI was $52.6 billion in 2010, $69.5 billion in 2011, and $60.5 billion in 2012 before falling off to $34.2 billion in the first nine months of this year.

The United States was officially the No. 1 source of FDI in Brazil in 2012, at $12.3 billion, and has also been the largest source so far this year.

* The CBBC report, based in part on interviews the group held with executives from Chinese companies and their Brazilian partners, said Chinese investments focused on natural resources "have plummeted" since 2011.

The report attributed the drop to "uncertainties regarding Brazilian policies," highlighting recent changes to mining laws as well as new restrictions on how foreigners buy land.

"These and other related policies are ... causing companies to hold off investment plans," the CBBC said.

* A report this year by the Inter-American Dialogue, a Washington-based think tank, indicated that Chinese financing of projects in Latin America as a whole also peaked in 2010.

The study, which tabulated loans from Chinese banks, found that financing rose from $13.6 billion in 2009 to $37 billion in 2010. It then fell to $17.5 billion in 2011 and just $6.8 billion in 2012, the last year available.

(Reporting by Caroline Stauffer and Brian Winter; Editing by Kieran Murray and Ken Wills)