If global warming is culprit, more melting, more fresh water and nutrients in world oceans and good sunshine may be the reason for higher productivity,my wild guess

Thank you but the ocean productivity is not increasing steadily. It shows a peak in 2010.

What about temperature, precipitation of 2010, any abrupt peak there also

Perhaps the answer to this question is the same as given in item:

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What are the expected effects of global warming on human migration?

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Mutantis mutandis, the answer can be fully exploited.

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How valid is this statement on spatio temporal scales. If this was true then probably SST, CO2, nutrients levels.

Read this

http://www.biogeosciences.net/7/621/2010/bg-7-621-2010.pdf and especially section 3.4 and 3.5

there are a myriad of physical factors that lead to increases and decreases in ocean productivity.